I'm back in the homeless shelter here, and homeless shelters will pretty much be how I'll be traveling the country for free or cheap. They're like the new hostels, basically. Some do have resident restrictions, but national shelter programs like the Salvation Army (wouldn't suggest it, if you're in the queer boycott) usually don't have such restrictions. There are shelters of higher and lower quality, in comparison. If you're looking for any particular shelter like being Queer friendly so so on, you'll have to do a detailed internet search on that. Staff is a factor as well. If you're discriminated against you may be able to press charges, but that won't fix where you'll be laying your head THAT NIGHT.
Other options are cough surfing, abandon builds, and various other things. These day, shelters are the safest option in a foreign place. Or course you should stay with kind people that you know, if that's an option in any area.
But, that's paranoid me. You live your life to be