Wonderful trip to the back country, Saint Guillhem du desert and more try https://www.wisud.com/fr/
An excellent wine tasting trip is with Bertrand Bosc: https://www.bertrandbosc.guide/
I heard excellent feedback on both from family and friends. Book early because they both fill up.
White tablecloth Restaurants:
Maison Marguerite maisonmarguerite34.fr
Le Petit Jardin https://www.petit-jardin.com/
L'Artichaut http://www.artichaut-restaurant.com/
Casual:
Umami-La Cinquième Saveur https://www.umami-cinquiemesaveur.com/
Roco et sa mère
Au Loup https://m.appero.co/#dae19345-587f-49ca-bff3-4f9443831809
and many, many more
Attractions:
the whole Centre Historique in which you could wander for hours. Look at the Salle Pétraque on the Place Pétraque and the medieval building next to it..
There are about 180 old mansions from the boom days (wine export and center of regional government)...followed by bust days when the vines died due to phylloxera.
Stop on the places filled with restaurants and cafés. These places used to have churches until they were destroyed in Religious Wars or the Revolution
Place de la Canourgue overlooking the Cathedrale
Art:
Street art is everywhere as are fountains.
Fine arts: Musée Fabre
Primitive art museum: Musée d'art brut
Contemporary art: MOCO and MOCO Panacée, both have good restaurants with outdoor seating
Gardens: Jardin des plantes founded to provide plants to the medical school
Old medical school building, oldest continuously in operation medical school in the world. Nostradamus was a student in Montpellier.
Gifts: available in all the boutiques in the historic center, especially near the Banquise ice cream store (best ice cream in Montpellier and possibly the world) 2 bis rue du Petit Saint Jean
Incredible toy store for gifts: Pomme de Reinette et Pomme d'Api 33 rue de l'Aiguillerie
Office of Tourism is on the Place de la Comédie English-language tour every Saturday