Some ideas of places to check out in Nancy:
Stanislas square
Art museum , on the Stanislas square
Opera of Lorraine, on the Stanislas square
Parc de la pépinière, next to the Stanislas square (again)
Cathédrale Notre-Dame-de-l'Annonciation, 56 Bis Place Mgr Ruch
Aquarium, 34 rue Sainte-Catherine
Villa Majorelle, 1 Rue Louis Majorelle (not in the center but accessible by bus)
Porte de la Craffe
Some ideas of restaurants (the ones marked with a € range from €40 to €55 without drinks). Many of them might require to book in advance.
Trattoria San Giorgio
Khao thip thai
Brasserie Saint-Georges
La petite cuillère
Les Bacchanales
Kung fu Nouilles
L'excelsior (€)
L'Arsenal (€)
À la table du bon roi stanislas (€)
27 Gambetta (€)
For drinks, there are many bars on place Saint-Epvre and in the area around the cathedral.