France

Reasons to go:

Architecture:

Old town of Toulouse
Little squares/crossing that made me pause and smile: Place des Tiercerettes, bifurcation of Pl. Dupuy next to La Halle aux Grains, crossing of Rue Ferrières and Rue Cujette, Place St Georges - a little square full of outdoor cafes.
Basilique Saint-Sernin de Toulouse - beautiful at night too

Museums:

Halle de la Machine - this place is actually much more awesome than a museum, especially due to the amazing team of people that make it happen. A must!
Musée Aeroscopia is still on my to-visit list.

Markets:

Marché Victor Hugo - great place to buy local specialities, and picnic in the nearby Jardin Pierre Goudouli.
Marché de Saint Aubin on Sundays - great place to buy local specialities, ethnic street food and more; and picnic on the steps of Saint-Aubin church.

Other stuff:

Graffiti - I used this map to find graffiti, including works by local artist Korail and Aryz.
La Belle Verte, the vegetarian restaurant focussed on local seasonal ingredients and non-sweet flavourful deserts, was where I had my best meal. Still on my to-visit list are Sixta and Le Grenier de Pépé.
Cocktails at Fat Cat.
Jardin des Plantes and surrounding green areas are very nice.

Notes:

Best place to stay - somewhere not far from Le Capitole.
Tisséo app works well for all public transport in the city; no need for physical tickets.

Nearby:

Romantic little villages liks Lectoure and Condom (the cathedral and L’1 Pour Tous vegan restaurant are not to be missed). Carcassonne, Cordes-sur-Ciel and Albi are still on my to-visit list.
The Sunday market in Montcuq village is nice.

Hiking and breathtaking views:

Estany Primer de Pessons in Andorra. An easy but stunningly beautiful circular hike from Grandvalira Estació de Ski Grau Roig to more than 10 lakes.
Hike in Gourgue d’Asque - a lush mossy forest, a totally different experience in the Pyrenees mountains.
Beautiful drives with hiking opportunities - Col du Pourtalet, Col de Tentes (hiking to Cirque de Gavarnie from there), drive to the end of D922 (hiking to Cirque de Troumouse from there), Col d’Aubisque, Col de Marie Blanque (with opportunities to buy local cheese along the way), drive into Andorra using C-28 in Spain.
May is a very special time to visit, when the mountains are covered in flowers and it is not yet too hot.

Other stuff:

Pic du Midi de Bigorre - eye wateringly expensive téléphérique, but it does provide the best view of the tallest mountain peaks. No hiking opportunities from there.
Cave of Niaux - 16,000 years old paintings. Book in advance as capacity is strictly limited to preserve the paintings. Nearby talc quarry and Lombrives Cave is still on my to-visit list.
The Odeillo Solar Furnace (Heliodyssee-Grand Four Solaire of Odeillo) has 9,600 mirrors that concentrate the sun’s rays on a point the size of a cooking pot to achieve temperatures upwards of 3,300℃. It was opened in 1970 and was used by space agencies to test high-temperature materials for nuclear reactors and space vehicle reentry. It is high on my to-visit list, but I’m not sure if it is still there.
Petit train d’artouste is still on my to-visit list.

Places to stay:

Pau is relatively big and has nice stuff - Halles de Pau market, Blend cafe for good breakfast, cocktails at Snag.
Argelès-Gazost is a lovely village with cheese shops and bakeries. Cauterets (on the way to Gaube Lake) is still on my to-visit list.
Avoid Lourdes.
Andorra la Vella feels like an airport, good for working-from-home only.

Traditional French food is generally not vegetarian. If you are vegetarian, expect to go heavy on cheese (the selection of goat’s milk cheeses is heavenly) and pastries (Tarte Tatin and Canelé are my favourites). If you are vegan, expect to frequent restaurants of other nationalities.
Most things close for lunch (shops, funiculars, tourist information centers, etc.), so plan accordingly.
ATMs of La Banque Postale don’t charge for withdrawals.