Montpellier eats well — the city sits on the Mediterranean, surrounded by Languedoc vineyards, with oyster beds at the Bassin de Thau and bullfighting country to the west. Expect lots of olive oil, garlic, herbs from the garrigue, lamb, and fish. Local specialities include brandade de morue (salt cod whipped with olive oil), tielle sètoise (octopus pie from nearby Sète), and petits pâtés de Pézenas (sweet-and-savoury mutton pies the locals trace back to Clive of India). The wines to ask for are Pic Saint-Loup, Terrasses du Larzac, and the white Picpoul de Pinet from the coast.
The historic Écusson is dense with bistros and brasseries — Place Jean Jaurès, Place Saint-Roch and Rue de l'Aiguillerie are good places to wander and pick somewhere from the terrace. Don't bother with the international chains around Place de la Comédie; walk a few streets in.