The guacamole and the sopa de lima are also good here and try a pitcher of ague de lima the fresh yucatecan citrus that is more like a bergamot than a persian lime. It's a good place to try Relleno Negro too.
If your staying in town the all the guide books recommend Los Alemendros and if your must (I wouldn't) then try the one in the Fiesta Americana as the one at Mejorada is just depressing. I'd try La Tradicion near the hotel zone or Chaya Maya before setting foot in Los Alemendros but I'd be just as happy with a couple of tortas from Le Smoking Club I as anywhere else.
I think that ordering the Mayan food on the menu at the Haciendas is almost always a good idea. The Starwood Hacienda hotels have very inconsistent food as the chefs come and go and the cooks who assist are from the villages...at least they know how to make the local fare. Even at the usually very good restaurant at Hacienda Xcanatun the Mayan food is often the best option.
But really you should go to the Mercado or one of the satellite markets at Santiago or Santa Ana or even San Sebastian for fast food and try the simple soups and tamales and the tacos. Cocina Economicas cannot be beat for lunch and you can find them all over town in every single neighborhood. Local women cooking traditional meals (not usually Mayan) in their homes or little shop fronts with a couple of tables and plastic chairs. You'll find them delicious and hospitable and you'd be hard pressed to spend more than $50 pesos for a hearty meal.