There are many amazing places for food, drinks, music, and/or dancing all over Havana. These are just some of my recommendations as a good place to start.
A note on the food: Cuban food is not like Mexican food. It’s much more like Puerto Rican food, actually. Don’t expect a lot of spice. They don’t eat spicy food here. Staples of the cuisine include plantains, rice & beans, and many potato-like root vegetables. Pork is usually a good choice when in doubt (I’ve never had a bad Cuban pork dish). As much as they tout their seafood in Havana, we didn’t love the shrimp or lobster anywhere we tried it (both the actual product, as well as the various preparations) — but the octopus (“pulpo”) was delicious, whether grilled or as part of a ceviche or carpaccio. Fish ceviche is also a good option on a hot day anywhere you go.
A note on the drinks: Rum is obviously the local specialty — made from local sugar cane for many generations. Therefore, rum-based drinks are the way to go — from the classic mojitos, to the fruity blended daiquiris, to the simple cuba libres (rum and coke with lime). They do have beer everywhere (sometimes it’s not on the menu, as it seems the selection always changes). The local beer is Cristal, but it’s not as easily-found as I would have thought. It takes very much like a Heineken, though — so I enjoyed the imported options more. You’ll usually have a Spanish and/or Mexican lager option.
Below is also a custom Google Map that maps all my recommendations and includes short descriptions. All orange pins are restaurants, blue are cocktail/food spots, and purple is for going out dancing. Per my post on the logistics of traveling to Cuba, however, I highly recommend exporting this (or any other custom Google Map), installing maps.me on your phone, downloading an offline map of the city, and importing this custom map to there. Instructions on how to do this can be found in this Going Awesome Places article on offline maps.