I grew up in Carrum which is about 10 mins from Frankston. Any of the bayside suburbs are gorgeous. There are always going to be bad crowds no matter where you live, its just steering your kids in the right direction.
Bonbeach, Chelsea, Edithvale, Aspendale, Mordialloc, Parkdale - all great places by the beach.
Personally I'd love to live in Frankston, as I live in the country now and as a city girl, crave 'civilisation'. Close to the beach, shops etc - the beach in summer down that way is awesome.
There are heaps of schools, not sure if you want public or private...

Paying for car parking wouldn't put me off an area - living in the city I have often paid $30 to park my car before, so 80cents or whatever isn't an issue for me.

There are some areas to avoid, The Pines has always been one of them.... these kinds of areas can exist anywhere though, I've lived in LOADS of different areas of Melbourne and honestly, Frankston isn't a place I'd ever really feel unsafe - unless perhaps I was night clubbing etc or out walking those kinds of streets at night, but those days are long gone.