Two types of college: publicly funded and privately funded, and you can use FAFSA for both.
Publicly funded (such as Pennsylvania State University and State University of New York, among many others) charge lower tuition for in-state students (because part of state taxes go to subsidize tuition). Financial aid offerings may also be different for instate and out of state (OOS) students- if so that will be spelled out on the college website.
Private colleges, such as UPenn and NYU, charge the same no matter where you are from (because they don’t get direct financial support from state taxes).
Both types of colleges will consider your application. Some public universities give a preference to instate applicants, and some limit the % of out of state students they will take, but they all take some.
College housing varies a lot by college. Most colleges offer student housing. Many- but not all- require first years to live on campus; at smaller colleges often most students live in college housing all four years; at larger universities, many live off campus for most/all of their college years.
There is nothing magic about going out of state- or away (depending where you live in PA, OH, MD, NY, DE or NJ might be closer than Erie, Pittsburgh, Scranton or Philly!). There are a lot of variables- what you want from your college experience, what’s affordable, etc. Emphasis on the affordable!