Given your interest in art, be sure to put the partly open-air museum Fondation Maeght on your list. It's just up the road from St-Paul.

(I'm biased towards Nice, as I bought a place there, but Marseilles could have worked as well). Regarding beaches, you can rent a chair in a private club in Nice or simply head by train to Juan Les Pins, where there is a long strip of sand, with a public section to the west. (Antibes also is another choice, just a bit further from the train station to the prime beaches on the other side of the Cap). Villefrance-sur-Mer also has a very accessible beach but it is more like large grains/tiny pebbles, but with a great view and very good beach club. If you have a favorite artist in the impressionist or post-impressionist vein, changes are there is a museum with at least a section devoted to them. (Note the Musee Massena, is not so much about art rather than Cote d'Azur history, special exhibition, and section on Napoleon. Best of Nice blog is another good choice for info).

Outdoor seating is ubiquitous in Nice (and throughout the south), choosing the right one to actually eat at can be a bit hit and miss, especially on the main squares/plazas and on Rue Massena. I recommend Le Plongeoir for an incredible view at lunch (it's an old diving platform on the water) and of the beach clubs, Le Galet or Beau Rivage. In the Old Town, le Comptoir du Marche, Bistrot d'Antoine or Bar des Oiseux are from the same owner and are moderate price with a higher standard, but more limited outdoor seating. If you want the view of the Cours Saleya market, Le Safari is the best choice there. If you have a specific interest, I can provide a more specific recommendation.