If Montpellier doesn't have a local speciality we know how to cook and you can find restaurants in every corner on the historical center.
My favorites places to eat is in "Saint Roch" place. There are plenty of good table here. This is yummy and not so expensive.
If you want an other place, try the bottom of the Aiguillerie's street. Restaurants like "Grillardin" or "Chat perché" are institutions in town.
If you want something different for a special date (birthday for example), feel free to ask.
Also, you can find all the good adresses in the local webzine "montpellier.citycrunch". It is in french, but if you don't understand, you can always translate the page with google ;)