Partly it will depend on when. For example, our favorite town on the Cote d'Azur, Menton, is the warmest city in France in midwinter. In the summer, however, it can be uncomfortably hot.

The Nice Airport is well-located for rental car access up and down the coast. Monaco is interesting, IMO a little soulless, there are great museums in Nice, and our fave place along the coast is the Ephrussi de Rothschild museum in Cap St Jean Ferrat - gorgeous gardens, really a glimpse into how the other 1% lived...

Without a car, quick train to Monaco (and Menton) is easy. But as Viajero says, a car really adds to the pleasure of the area.

If you want warm and far, what about Madeira? LGW-FNC is over 1500 mi, vs. 600-something to Nice.