Czechia

Reasons to go include:

1. Prague

David Černý art and architecture:

Musoleum David Černý is the most exciting thing I saw in Prague. This is a very 18+ art gallery. Start from the 4th floor and work your way down into the basement. When I visited, this area was in the middle of a construction boom, arriving at this tram stop (50.051467, 14.409174) was the best way to get here.
Fragment apartment building (50.097032, 14.461821) in Karlín, featuring Lilith sculpture by David Černý, is very architecturally exciting and totally worth the detour. The nearby Etapa brunch place might be nice.
David Černý sculptures scattered around Prague: Peeing Characters (50.088073, 14.410224), Babies (50.084106, 14.408375), Franz Kafka Rotating Head (see it during the day and on the hour), Butterfly Effect, Man Hanging Out. Embryo (50.085151, 14.414504) is to be seen after dark. Horse is on my wishlist, somewhere around (50.080942, 14.42617).

Art galleries:

Mucha in Palace Kaunitz Museum (on Panská street) is a great place to see works by Alphonse Mucha. At the back of the gallery you can watch an interesting biographic video in English. Reviews say Mucha Foundation Art Museum (on Na Příkopě street) is small and contains mostly reproductions.
National Gallery Prague Trade Fair Palace is huge, you’ll have to be strategic or it will take the whole day. Start from the 4th floor and work your way down. See the list of permanent and temporary exhibitions to decide which other National Gallery buildings to visit (e.g. Schwarzenberg Palace or Sternberg Palace).
Kunsthalle Praha - temporary exhibitions. I visited on Friday evening when it’s open until 21:00.
On my wishlist are galleries in Holešovice area: DOX Centre for Contemporary Art, Bold Gallery, The Chemistry Gallery, Trafo Gallery. Also Museum Kampa.

Walks:

Architecture of the Old Town (Staré Město): My favourite architecture spot is at (50.087382, 14.428467) where you can see the Municipal House, The Powder Tower and Czech National Bank. My other favourites are National Theatre, Clam-Gallas Palace, Dancing House, Rudolfinum, Prague New City Hall, this building (50.085993, 14.423245) and buildings at this intersection (50.084184, 14.423474). Staroměstské náměstí square is where all the famous stuff is - Church of Our Lady before Týn, Prague Meridian, Prague Astronomical Clock, The House at the Minute, Rottův dům, Týnský dvůr square. Vinok Sculpture (50.090593, 14.425879) is great.
The Jewish Quarter: Architecture around the Staronová Synagoga. On my wishlist: seeing the interior of the Spanish Synagogue, exploring Old Jewish Cemetery, Jerusalem Synagogue.
The evening walk through lit up highlights: Walk through the Prague Castle (free, open 6:00 - 22:00) from this gate (50.091796, 14.405296) to this gate (50.090068, 14.39804), seeing magnificently lit up Saint Vitus Cathedral. Nerudova street is pretty and St. Nicholas Church Malá Strana is lit up. See Yellow Penguins (50.084308, 14.408949) glowing in the dark. Cross the Charles Bridge. See the Embryo sculpture (50.085151, 14.414504) by David Černý. You could continue to Dancing House which is also nicely lit up.
Holešovice area of old factory conversions: My favourite bit was the walk between (50.103175, 14.449347) and (50.101951, 14.449332) - graffiti and cafes like Vnitroblock. The area between (50.100668, 14.446093) and (50.098356, 14.445851) contains Holešovice Market, some galleries and whatever else is going on. A new residential area around (50.106249, 14.450568) is architecturally interesting, and there is EMA espresso bar. Osada is a fun place with nice coffee.
In the morning, bring carrots to Střelecký island and find the local nutrias.

Prague notes:

On my wishlist: The old wastewater treatment plant, Vyšehrad Cemetery, Olšany Cemetery and New Jewish Cemetery, Plečnikova Vyhlídka viewpoint, Letna park and Prague Metronome. I’m looking forward to Vltava Philharmonic Hall near Vltavská metro station that could be built soon.
Where to stay: I stayed in a nice residential neighborhood just north of Hradčanská station, which is a convenient transport hub (metro, many trams and a 20min bus to the airport). Apart from great transport connections and an Albert supermarket, I enjoyed great value all-you-can-eat lunches at Indian by Nature II and vegan cruffins at Kafemat. But next time I’m staying in Letná neighbourhood - the land of great coffee.
Seeing a performance: Some of the plays at Švanda Theater in Smíchov have English subtitles, the balcony is the best place for reading the subtitles (especially the middle of the first row). Image Black Light Theatre does fun circus performances (it is not a theater).
Public transport is based on paper tickets. You can buy a ticket with tap to pay after boarding the tram (the orange machine, not the yellow ones). To use the metro, you have to purchase a ticket at the station first, then validate it at the gate, before boarding the train.
Coffee: My favourites are format.coffee (there is more seating at the back) and 25,2 rpm (ask for nice non-default beans), both in Letná neighbourhood. Onesip coffee is amazing. Coffee Room Celetna is great, upstairs seating is very nice. On my to-try list: Letec espresso bar, Version Coffee, Café Tone, Merrybeans, Dos Mundos Coffee Roastery, Acid Coffee, Ye’s kafe, Typhoon Coffee. I was excited about Mazelab coffee, but their cheapest flat white (~6 USD) was underwhelming and the more expensive ones (70 to 450 USD) created a strange atmosphere of people coming in and leaving after seeing the menu.

2. Brno

Water Tanks under Žlutý Kopec - this was my favourite place in Brno. Arrive at opening time for the most atmospheric visit. Free audio guide available for download.
Ossuary at the Church of St James - it is very small, it won’t take long to visit. Photography is allowed. Entrance is just outside the church, down the stairs. For me this was a good alternative to Sedlec Ossuary in Kutná Hora.
Architecture: Zelný Trh square (don’t miss the cute fountain at (49.191909, 16.608816)), Dominikánské náměstí square and Náměstí Svobody square (especially this (49.194602, 16.608862) building). The stonework on the east entrance of the Old Town Hall is fascinating, give it a long exploratory look before you get distracted by the Brno Dragon. There are so many pretty buildings, don’t miss this one (49.204231, 16.595177), the one adorned with sunflowers (49.19816, 16.593852) and Mahen Theatre. Explore interesting courtyards at (49.193911, 16.605893) and (49.193029, 16.606652). See Waiting Adam statuette (49.197351, 16.605156), this statue (49.197481, 16.607102) and the horse across the road. Walk past Kalina Gallery to see some contemporary art. This spot (49.199155, 16.60668) in Moravian Square Park seems to be the favourite evening hangout place for locals, in winter it becomes an ice skating rink.
Moravian Gallery. Permanent exhibitions are free to visit in these 3 buildings - Governor’s Palace, Pražák Palace and Museum of Applied Arts.
Brno Astronomical Clock - try to be here just before 11:00 to observe the daily ritual.

Brno notes:

Other things if you have more time: mummies in the Capuchin Crypt, view from the Old Town Hall tower, Bunker 10-Z, Kryt Denis, Labyrinth Under the Vegetable Market, Špilberk Castle.
Public transport in Brno is tap-in with bank cards, tap-out is optional (it allows you to get a cheaper ticket for a short journey). Bus 21 gets you to/from the airport really fast.
Food: Saffron Persian Food - incredible Iranian food, mostly vegan with options to add meat or yoghurt, best all-you-can-eat lunch in town. Vegan AF Ramen - their Tantanmen Temptation ramen kept me coming back. Falafelo makes falafel. SKØG has great vegan breakfast options. Dezertína for pastries, Mama Stella for sourdough, JEŠTĚ jednu for gelato.
Coffee: The Roses on Benešova street was my favourite. Monogram Espresso Bar is ok. Next I’d try Pikola espresso bar, qb scuk and Krok espresso bar.

3. Ostrava

Dolní Vítkovice - this former ironworks site was my favourite place in Ostrava. The area has no gates, it is free to explore 24/7. I enjoyed exploring it after dark and then again in daylight. Tours are in Czech only. I did the 100 minute tour (book in advance) of the blast furnace and Bolt Tower, and I’d say the additional things you get to see by joining the tour are not worth the time spent. You can listen to this free audio guide as you walk around the area by yourself. To explore more mining heritage in Ostrava, there is also Mining Museum Landek Park (pay for entry to the museum with indoor and outdoor areas, or join a tour in Czech to go into the mine) and Důl Michal mine (only tours, only in Czech).
Architecture: Masarykovo náměstí square, New City Hall, Evangelický Kristův kostel church, Kostel svatého Václava church, Antonín Dvořák Theatre, this (49.834825, 18.287646) building, Plato gallery building and Ostravská Madona street art.
Art galleries: check websites of Plato municipal gallery of contemporary art and Gallery of Fine Art in Ostrava for current exhibitions.

Ostrava notes:

Kikafe Ostrava is where I found the best coffee; next I’d try Shothouse and PetPunk. Hogo Fogo Bistro (food) and Essko Espresso Bar (both closed on weekends) are on my wishlist.
I used this blog by Lucie and Martin.
Public transport in Ostrava is tap-in with bank cards, tap-out is optional (it allows you to get a cheaper ticket for a short journey).

Notes:

To explore the landscape of sandstone karsts on the border of Czechia and Germany, we used this (50.88603, 14.235558) free parking and walked into Germany to hike in Saxon Switzerland National Park. Bohemian Switzerland National Park (the Czech size) suffered a devastating fire in 2022.
I had a 99% cashless experience in Czechia. The only time I needed cash was to pay a per-night city tax to my accommodation in Prague.
Unlike other ATMs, KB (Komerční Banka) did not charge me for a withdrawal with a foreign card.
Czech Railways make buying (and refunding) tickets super easy. The main station is “hl.n.” for hlavní nádraží.
Bolt is the most common Uber-like app, but the public transport is so good that I hardly ever needed it.
Albert and Billa supermarkets are good.
Coffee: Flat white is the only espresso-based drink that is double shot by default.