Unfortunately, I don't believe there are many such places. If one is living in their tent, car, or similar situation, there are very few places where one is even allowed to exist peacefully without spending a few dollars, let alone take care of one's hygiene.

Libraries are one of the precious few places where one is not charged on entry or otherwise expected to buy something. Even public parks are increasingly hostile to the homeless, but often no real alternatives are offered. And I think that's a shame.