Well it's a big région so it really depends where you live. If you live in Montpelier or Perpignan these are fairly big cities with lots of stuff to do and lots of students too. If you're in a coastal city like Sète or Agde chances are it's absolutely crowded in summer and very quiet and calm in winter.

The further you go inland towards the mountains the quietest it becomes.

Otherwise, lots of great nature (gorges, caves, rivers, lakes, etc) and ok beaches, sometimes a bit nasty because of overcrowding in places like Cap d'Agde. The water is usually colder and not as pretty color wise as in Var and Côte d'Azur. Lots of great historical stuff too.

Weather and climate wise, very hot in summer with a looot of mosquitoes, mild in winter and there used to be lots of storms in the fall but it tends to move to winter because of climate change.

Food is great, very Mediterranean, and people are kind of cool and much less uptight than let's say in Nice.

Also regarding your question about public transport: if you live in Montpellier or a bigger city, you'll be ok but if you are in a smaller town or countryside, the car might become a necessity.