/diy/ - Do It Yourself

Is it safer to hang out at 24 hr places during the night, and sleep in the day just in a park or something?
That's what I'd do if I was in your situation. Of course, this cycle might disrupt work.
You say you have a job? For god's sake do not lose this job. And what the hell, you may as well lower your standards and try get a job at subway or a fast food place or something... Until you get enough money to get your own place. Working the graveyard shift may help eliminate the necessity to find somewhere safe to sleep for the evening.

Also, the library is probably a good place to hang around. Some gyms, colleges, hospitals etc. have showers I s'pose that you could probably hit once or twice or more with a fair while in between if you just walk around pretending like you're supposed to be there.
The worst part, I imagine, would be being looked at like you're someone to be avoided. That's why personally I'd place personal hygiene/grooming high up on the list. And a job...
But then again, I'm not homeless now and I barely do those things.