Greece

Reasons to go:

1. Athens

1.1 Koukaki and Makriyanni

This is the best area for both short and long stays in Athens.
National Museum of Contemporary Art Αthens - a great way to spend a Thursday evening, when the museum is open until 22:00. Free entrance every first Thursday of the month after 18:00.
Delirium Athens street art gallery - a small art gallery featuring skulls, surrealism and 90’s comics. Swing by even if it is closed - you can see a lot from the outside.
Church of Saint John - cute little church.
Arch of Hadrian - a nice arch and a good view of Temple of Olympian Zeus.
Geor. Olimpiou - pedestrian street lined with bars and restaurants packed with locals. Nearby Strange Brew Taproom & Bottleshop has a great collection of beers.
Dyo Dekares I Oka - a great place for traditional Greek food; better for lunch as best daily specials will run out by dinner time.
Peas Vegan and Veganaki - good vegan restaurants. For a vegetarian moussaka head to Onos Taverna.
Fika coffee & croissant - awesome bakery and good coffee. No toilet.
Django Gelato Athens - the best gelato in Athens. I also had Oggi Officina Gelato Gusto Italiano, Solo Gelato and Le Greche on my wishlist, but instead I kept coming back to Django.

1.2 Acropolis, Plaka, Monastiraki and Psyrri

This is the souvenir city, great for a day time visit but avoid staying here.
Areopagus Hill - a big rock with great views of Acropolis and the whole of Athens. A great place to start before entering the Acropolis.
Acropolis - the most iconic landmark of Athens. Use this entrance (37.971432, 23.723817) to explore Acropolis before it gets too crowded, after exploring the slopes you can leave through this entrance (37.969692, 23.728994). Avoid resellers, buy the tickets on Hellenic heritage website. If you know you’ll want to explore more archaeological sites, consider buying 5-day Combined Ticket.
Acropolis looks magical when lit at night. Luckily you can see it from almost anywhere. Horologion of Andronikos Cyrrhestes is also beautifully lit up at night.
Filopappou Hill - great for a long walk. The best 360 view of Athens is from Philopappos Monument, but there is more to discover - Holy Church of Saint Demetrios Loumbardiaris, Dorides Telescope (Τηλεσκόπιο Δωρίδη), etc.
Anafiotika is a scenic tiny neighbourhood on the Acropolis hill. You can enter through (37.971432, 23.723817), but locals are not thrilled about their homes described as photogenic in Lonely Planet.
Churches: Panagía Kapnikaréa Church - a cute little church on a roundabout. Agia Paraskeue (37.978858, 23.723616) - an even smaller church. Holy Church of the Virgin Mary Gorgoepikoos and Saint Eleutherius (37.975062, 23.730017) - smaller yet, hiding behind a big one. Church of the Sacred Power (37.97519, 23.732015) - the smallest church in Athens? And now, Holy Church of the Dormition of the Virgin Mary Chrysospileotissa looks enormous for comparison.
This is a great area for graffiti hunting. One of my favourite spots was (37.978758, 23.721953).
On a Saturday afternoon, this (37.981472, 23.728649) is a popular skateboarding spot.
Food shopping around Varvakios Central Municipal Market: Η στρούγκα του Μοριά - for-locals cheese shop, try fresh anthotyro cheese (similar to ricotta). The Monastery Cellar (Το Κελάρι της Μονής) - shop of monastery produced goods, here you can buy honey or fruit preserve for your anthotyro.
Myller Coffee Shop - great coffee in a lovely square overlooking a church.
heteroclito - awesome wine bar, by-the-glass menu features useful descriptions.

1.3 Thiseio and Petralona

This west of Acropolis area is for-tourists for as long as you can see the Acropolis, but then the normal life resumes.
Iraklidon - a charming pedestrian street. Lost Roots Wine Bar seems popular with locals.
St. Catherine Church of Petralona - a cute church.
Ubuntu - great coffee. Across the road Oliver’s boulangerie croissanterie has great spanakotipa (spinach pie) and bougatsa (custard pie) fresh out of the oven.

1.4 Metaxourgio, Keramikos and Gazi

Perhaps the coolest neighbourhood of Athens.
★ Industrial Gas Museum. At this entrance (37.977379, 23.713232) you’ll find info on how to buy tickets online (very cheap) and the information for a self-guided tour of the museum distributed across many buildings.
This is a great area for graffiti hunting. My favourite spots include (37.976669, 23.712674) and (37.983399, 23.718595).
Los V (vegetarian and vegan) and Veganistan (fully vegan) are great restaurants. Both are located just off Salaminos - a lovely pedestrian street.
To see a different side to Athens, use Fallen Aviators Monument, a cool statue, as an excuse to walk along Iasonos and Kolwnou - streets lined with brothels.
On my wishlist - Benaki Museum Pireos (the modern art branch), Municipal Gallery of Athens (free) and Pyroliki restaurant.

1.5 Exarcheia, the anarchist district of Athens

★ National Archaeological Museum - the collection is both historically significant and enchantingly beautiful. Don’t miss the Antikythera Mechanism in room 38. You have several free audio guide options - Rick Steves audio guide app, NAM audio guide app (didn’t work on my Android version) and a physical audio guide you can pick up at the information desk (you’ll have to leave an ID as a deposit; if you happen to have wired headphones you can use them for extra convenience, just insert them half-way into the audio jack). Apart from the tiniest bags, everything else has to stay in the free luggage storage, which makes this museum an ideal place to explore on the day when you have nowhere to store your bags. This is a true treasure trove - you might prefer to visit this huge museum twice, instead of visiting both this one and Acropolis Museum.
This is a great area for (political) graffiti hunting. This (37.984879, 23.735062) is a good starting point.
Ama Lachei was my favourite meal in Athens. Book in advance to avoid disappointment.
Tivoli - another great restaurant.
Stani - have a breakfast in a dairy shop. Yoghurt with honey and walnuts is an obvious choice.
Boken - great coffee. I paid extra for the speciality beans and it was the best coffee I had in Athens.
On my wishlist: Hellenic Motor Museum, Cafe Bar 67 (Ukrainian cafe), Tanini Agapi Mou (wine bar).

1.6 Kypseli

Fokionos Negri - this tree-lined pedestrian avenue is the focal point of the neighbourhood.
Platia Agiou Georgiou - a lively roundabout.
Coffee lake (λέικ καφέ) - a nice coffee spot.
Πεδίον του Άρεως - a lovely park.
This is a great area for graffiti hunting. One of my favourite spots was (37.995504, 23.735196).

1.7 Kolonaki and Pangrati

Mount Lycabettus - fun to climb and amazing 360 views of the city. From here you can see great domes of Holy Church of Saint Dionysius the Areopagite and Church of Saint Panteleimon of Acharnai.
Academy of Athens (37.980096, 23.734109), a university and Vallianio Mansion - three beautiful buildings in a row, especially impressive when lit up at nights.
Benaki Museum of Greek Culture - the collection is a bit random, but it is a great way to spend a Thursday evening in Athens (when the museum is free and open until 23:00).
★ Dromeas (The Runner) sculpture near National Gallery - my favourite sculpture in Athens. And there are more sculptures in the gardens west from it.
Athens National Garden is lovely. Don’t miss the turtles at (37.973683, 23.738056).
First Cemetery of Athens - beautiful sculptures. Entrance at (37.964733, 23.735502), free.
Ombrela Cafe Brunch Bar - great breakfast/brunch and coffee.
Redd Coffee and KUDU Coffee Shop Pagrati are both great.
On my wishlist: National Gallery Alexandros Soutsos Museum, Basil & Elise Goulandris Foundation (another art museum), going for a run at Panathenaic Stadium (between 7:30 and 9:00, you’ll still have to buy a ticket), To Tsai (tea shop).

1.8 Piraeus and the beaches

You can get here by tram. T6 tram goes from Syntagma station to the coast, terminating at Pikrodaphne. Exit T6 tram towards the coast to catch T7 tram to the beaches; or exit towards the city to catch T7 tram in Piraeus direction. While not the fastest way to travel, this is the scenic route. T6 tram cuts through the city and skirts Holy Church of the Dormition of the Virgin Mary. T7 tram travels along the coast; don’t miss this tiny church (37.933115, 23.692584).
★ Stavros Niarchos Foundation Cultural Center - the new home of National Library of Greece and Greek National Opera. Free. Arrive before sunset to explore Stavros Niarchos Park (entrance at (37.942113, 23.695561)) and the great views from the top of the building. There is a free audio tour too. But don’t leave until after sunset - the building looks magical when lit up, as does the fountain and the views from the top. Don’t miss the fountain shows taking places every half an hour, for about a minute.
Grove of the Prophet Elias - climb this hill for great views. From the viewpoint towards the north (37.940821, 23.655597) you see massive cruise ships parked right in front of the Holy Trinity cathedral, and Port of Piraeus. From the viewpoint towards the south (37.938614, 23.65657) you see numerous marinas.
Sea Turtle Rescue Centre - volunteer-run rehab facility for injured sea turtles. Volunteers run short tours explaining the work they do at the centre and showing the turtles. See the x-rays of turtles on the wall. Welcoming atmosphere, with no pressure to donate.
Glyfada beach stretching between (37.873708, 23.732246) and (37.864598, 23.741086) was my favourite.
Ellinikon, a new coastal neighbourhood, is under construction. This will soon be an exciting place to visit, but for now tram stops between Loutra Alimou (37.902227, 23.719575) and Platia Vergoti (37.871488, 23.735223) are not operational - it is a construction site.
Emagie - great restaurant.
On my wishlist - Archaeological Museum of Piraeus, Hellenic Maritime Museum.

Notes:

Museum tickets are cheaper between November 1st and March 31st. That’s a hint for when is the best time to visit, when it is not overcrowded. It is also the time when oranges decorate most of the streets. These are bitter oranges and they are full of seeds, so locals don’t touch them. But I like bitter, so I enjoyed juicing the ones I found on the pavement.
Athens public transport works with contactless card payments. Tap in and out for metro, only tap on for buses and trams. Public transport was sufficient for me, but there is also Uber and Freenow.
I had a completely cash-less experience in Athens.
Before you go, read about polikatoikias, a ubiquitous type of building in Athens, to fully appreciate them when you see them.
Look out for graffiti by INO and public artworks be Christina Saradopoulou.
Sklavenitis was my favourite supermarket chain.
Tap water is freely available in all restaurants and cafes. Some places still put a plastic bottle on a table, but it is totally fine to ask for tap water instead.
Food and drink: Spanakotipa (spinach pie) and bougatsa (custard pie) make for a great breakfast. Apart from ubiquitous feta, I loved fresh anthotyro (similar to ricotta) and grilled mastelo (similar to halloumi); and there are many more cheeses on my wishlist - metsovone (smoked cheese), manouri, kefalotyri, etc. If in a wine bar, look out for xinomavro reds.