Real Mexican food has made inroads into Tampa's dining scene steadily for past few years. My primary criteria is the cheese. Cheddar cheese indicates Tex Mex. White farmer's cheese indicates something much closer to authentic Mexican.
Las Tucanes (as in Toucan Sam of Froot Loops fame) is a recent addition on Hillsborough avenue a few block east of Nebraska avenue. I must say, I was very impressed just to find Carnitas on the menu, never mind tongue tacos, etc. The Carnitas are excellent, as are the barbacoa tacos. Tamales are excellent, one of my favorite Mexican dishes, stuffed with turkey. All of the aforementioned foods were very cheap. For a pricier and more familiar treat, try the fajitas. Very good.
Despite the just hatches status, service and quality are quite good.