La Teresita, in historic West Tampa, is the last great Cuban outpost in the city. The city guides will tell you to go to the Columbia, but La Teresita is strictly locals only.
The counter-service La Teresita is comfortable and not so big, with stools that squeak and plenty of toasted Cuban bread for you to eat. The name of the game here is tons and tons of food for little to no scratch. You can eat a huge bowl of black bean soup, a large Cuban sandwich, and a serving of flan for $6. The black beans & rice are legendary.
The clientele is as varied as anywhere else in Tampa. You'll eat next to migrant workers new to the country, a South Tampa businessman with his entire family, a few senior citizens, girls filling up before they hit Ybor to dance, and lots and lots of Spanish-speakers who are friendly and talkative.
The hours are pretty extended (for Tampa), and Friday and Saturday it's 24 hours. Everything is good. You will not be disappointed.