In La Habana you won't find huge supermarkets like the ones we are used to, but local markets are scattered everywhere and are just perfect if you are looking for mango, aguacate, platano, guayaba, malanga....
These are the best markets in La Habana (for me)...
Boutique market, between 19 and B
This is probably one of the best markets in the city: it is not as cheap as the other ones, but compared to western standards it really affordable anyway. Here you can find the best and the freshest products, even the ones that are not always available in other markets (eggplants, tomatoes, strawberries...)
Outside this market you can also find a CADECA (casa de cambio) in case you need to change your money
One of the cheapest markets in town, between calle 19 y K
This is one of the cheapest markets you can find in the Vedado. It's really big and you can find a huge variety of products, ranging from fruits, vegetables, rice, bread, sweets...
You can buy a mango or an aguacate for 20/30 cents of euro (4/5 pesos cubanos)
The most familiar market, between 21 y J
This is my favorite market in La Habana, not because it's particularly big, or particularly cheap...but I used to buy here almost everyday and I always had great attention; you may not always find what you want everyday, but when you are in Cuba you just learn to appreciate what you have, instead of complaining for what you are missing .
Markets are usually open from 9:00 to 17:00 everyday from Monday to Saturday, and from 9:00 to 14:00 on Sundays