I'm not familiar with all of the eastern ones, but definitely in the west you will need a car. "Close" in Western terms might be anywhere from 30-100 miles. The eastern ones with which I'm familar are also not close enough to major hiking areas to do without a car.

At Seattle or the two Oregon schools, what you want is a clunker-looking car, which is less apt to be broken into. Car-clouting at trailheads is definitely a problem here in the Northwest. I suspect it is elsewhere, too, although evidently not so much in the Rocky Mountain states.