Your best bet is the Mercado de Productores at La Feria Ganadera which is on the Malecon (not sure how many kms to the west) near the Presidente Factory. I think the area is called El Cacique. Veg and fruit there is fresh and cheaper than the supermarkets, but if you are obviously foreign beware being charged gringo rates!
I am not sure if it is on every day, it is defintely there all weekend. I tend to go on Sunday mornings and it is a fairly pleasant place, although so much more could be done with it.
If you have kids it is a nice place for them to see farm animals and there are several people offering horse and pony rides.
There is a smart restaurant there as well as several comedores populares.
There are also markets in other parts of the city, like Ave. Mella surrounding the Mercado Modelo crafts and souvenir market.
Chiri