Hello,
Splitting your time between two areas depends on how much time you will be in the area.
For one week, I'd stay in one town or city...
Nice...for the city life, boardwalk , old town (was a bit grittier last time we were there), museums, excellent train connections all along the coast.
We once stayed in Villefranche-Sur-Mer, with a car, and drove to Monaco, Eze, visited Villa Ephrussi de Rothschild, Nice, and even Genoa, Italy. Don't forget to take the coastal hike from Cap Ferrat.
You will find beautiful coastline and lovely architecture all along the riviera.
If staying, for 2 weeks, then staying in two locations makes more sense.
FWIW, our first time in the area was in March, and I only needed a light leather jacket for the evenings.