Been awhile now since I was there but Jax Beach area in Florida seemed pretty decent. Lots of resources for homeless. Weather is warm all year round. Only issue with weather is the daily thunderstorms and humidity. Takes a couple of weeks to get accustomed to it but once you are you can tolerate any heat anywhere. I wasn't traveling or homeless when I lived there. But I did work a job that took me all over the city. I would talk to homeless and the traveling kids almost everyday. None of them were starving and most of them seemed to be happy or at least content. When I drove home along I-295 everyday there would be lots of them at the major exits leading to westside and the towns surrounding the city. The ones I talked to claimed to panhandle my daily salary in just a few hours at the morning and afternoon rush hours. The police do not really bother them from what I know.
If you're willing to work a regular or part-time job there are plenty of opportunities in the city. I did landscaping work there for a couple of years and the pay was decent. Did not need a bank account. There was a check cashing place right next to our home base. Got hired off the street and started the next day. They hire in August and September every year. If you can make your way into the city soon you should easily find something. If you don't want to work out in the heat there are plenty of indoor gigs in the city as well. I was making enough to support myself and a girlfriend. Rent isn't insane like other cities I've lived in. Lots of people looking to sublet. Public transportation in cheap and decent. Most of the city and outlying areas are walkable. The roughest areas and open air drug markets are easy enough to avoid.
All that said I left that area for a reason. I will probably never return and I've heard on here that it's hard to get into and out of Florida without a car of your own. I just thought I'd mention JAX because it sounds like you want to settle somewhere for a few months and stack cash. JAX treated me fine in that respect and the lack of cold/bad weather excluding the daily thunderstorms appeals to me. Being stuck out in the elements isn't that bad when you don't have to deal with the cold. Lots of people I met in JAX were camping either in the woods or right in the city. The cops didn't bother them from what I saw. There aren't massive tent cities like out west (yet). JAX had a lot of places handing out free food to homeless, offering shelter, and employment. One of the old crack heads on our crew would throw an old jacket on and get a bag of the free food from time to time. The food was good. They even gave out fresh fruit and hot meals.
JAX beach seemed like the best spot in the city. Just avoid the gated communities and rougher areas and you'll be fine. It's a good place to stop if you plan to go deeper in Florida. JAX is more southern than the rest of the state. Florida is backwards. The more south you go in that state the more unlike the rest of the south it is. Just be aware that the heat is sometimes unbearable and the woods is different down there. Often times you can't see your feet and you'll be swarmed by flying needles any time you step into it. I knew a few people that had been camping in the woods around JAX for years and claimed it wasn't that bad. But I wouldn't do it. I also saw a lot of people set-up under highway/interstate overpasses and bridges. One guy I saw near a property we maintained lived there for years without being bothered.