Promenade des Anglais runs along the sea front, and is the place to stroll in the early afternoon. The palm-lined road runs past most of Nice's main art deco buildings, and is a great place to soak up the sun and the culture in a relaxed way.
The Hotel Negresco dates from 1906, and is the most famous and grandest hotel in the city, and has an elegant coffee lounge inside where it is possible to take afternoon tea in surroundings as refined as the Ritz in London - only with better weather outside the windows. Be sure to dress smartly as otherwise you won't get past the doorman.