Northwoods is one of the top leagues that takes players from P5 schools, so yes, it fills up. A few years ago (and maybe still), they needed pitchers toward the end of the summer, though.
There are many other leagues, there's a pretty good list here, with links to the league homepages:
https://www.thebaseballobserve...r-collegiate-leagues
They run the gamut. Some of the leagues provide food and housing with host families, others provide dorms or apartments, some don't provide housing and are local-based. Some charge players a fee (like travel ball), some do not. Some provide local summer entertainment and are a popular local draw, others are purely playing games on high-school fields with hardly anyone watching.
Maybe @hokieone will add some advice, he is a summer league manager.