There are both "residential" and "commuter" colleges. For instance in my locale, the Big Ten university is mostly residential for undergrads (served by large student rental neighborhoods), and the housing typically chosen by grad students has decent access to the bus service, or bike-friendly routes.

There's also a community college that serves a lot of commuting students, and has none of its own housing.

The regional colleges have more commuter students, since you can save a boatload of money by living at home, but also probably don't have such severe parking problems -- land is cheaper.

This really depends on the college town. In East-Coast urban cores, most students won't be able to afford to park at any time. Everywhere else in USA, they have free parking where they stay, and also they're culturally conditioned to consider walking or biking to be beneath their station, so they'll consider free parking near their classes to be their birthright.

Which university? I've never been on a major college campus where it was even possible to park near the classroom buildings, much less practical. I live a few blocks from a Big Ten university in the Midwest. When classes are in session, the extensive rows of bike racks are stuffed full of bikes, to the point where illegal bike parking is actually a problem.

What I described is certainly the situation at e.g. Illinois, Indiana, and Nebraska, to name three "Big Ten" schools. I suppose I haven't done a complete survey, however. There are lots of other, smaller colleges where this is also true.

In my home town the local community college was a 45 minute drive from my parents house. I couldn't afford to move in to the city just to go to school. People who move to attend college are the exception not the rule, by the numbers.