The problem with him living in a tent and thus being 'of no fixed abode' is that Sirius is told by Dumbledore at the end of GOF to go and round up the old crowd, and 'lay low at Lupin's place'. I'm not sure he'd say that if he wasn't sure where Remus was.
Finding a deserted forest ... uh ... not possible in UK. He would never be able to take that chance, or else Dumbledore would have let him roam free in the Forbidden Forest. He would have to be somewhere with strong walls and locks.

I would have him with a place to live. You can do this two ways. Either he lives in his parents' house which was left to him. Or his parents bought him a small flat before they died. I've seen the former used in several stories, and I used the latter in one of mine.