Are we allowed to stay in hostels?

My friend and I want to go on a little roadtrip, particularly to San Diego. We just found out about hostels, since it is very cheap. However...I can't really figure out if hostels are just for international students or for everyone (i.e. college students). We're from California, but not San Diego. Also...what are your experiences with hostels? Any tips/suggestions? Thank you so much :)