Getting around within the major centres on the Côte-d'Azur is easy. The bigger ones - Nice and Marseille - have effective and cheap public transport (both trams and buses). The smaller ones like Monaco, St-Tropez and Cannes are eminently walkable. Cannes and, especially, Monaco also have good local transport, should the walking get too much.
St Tropez is much less good on buses. Then again, it's only the size of a large village - so spending money on public transport would be extravagant, even for a place with such a lavish reputation.
Travelling between these places on the coast is also pretty trouble-free ... especially between Monaco, Nice and Cannes. They are all linked by a cheap coastal bus service and a barely more expensive rail service. Getting along to St Tropez and Marseille is slightly more complex, but still quite do-able by public transport.
Rocky and rugged
It is, though, when you turn inland that public transport shows its limitations. Buses run to certain inland towns and villages - but they rarely go to all the places you'll want to visit and, even if they do, their schedules are unlikely to suit you.
For these trips, you really should consider hiring a car (see Provence car hire).
But, if you do hire a car, please take it steady. Back from the coast (and, indeed, on the coast in some parts) Provence soon rises rocky, rugged and a little wild. Roads can be narrow, sinuous and steep - and not all precipices qualify for barriers.
And, if you have the mildest problems with vertigo, don't even think of driving along the Verdon Gorges. This is as near as you can get in Europe to driving along the lip of the Grand Canyon. It scrambles the senses of those with no head for heights - which is bad news if you're at the wheel.
Otherwise ... well, happy motoring.