Is there a law in the us or anything that is close to the right to roam act in the uk?

There are places, like state parks and camping sites that will allow you to do some of those things but a lot of public places won't allow you to just start a camp fire and hang out like the way that you are describing. You would have to find a designated area for that and some of these places you even have to pay to get in. You could also see if someone with private land would allow you to use their property but still you have to be careful, especially in city limits in some states you can't start a bon fire, burn trash or leaves or anything like that without a permit, you have to be out in the country for such things.