There are tons of inexpensive apartments around JAX. Some are a bit more 'hoody than others.
My friend lives here:
called hunter's way. It's in Mandarin ,which is a pretty nice area. They're all newly painted on the outside, and the allow pets (dogs up to 50lbs). They're inexpensive, i think she pays like $700\month. You'll likely want to keep yourself on the East side of the St John's river.
I don't know if you want to keep your boat on a trailer, or rack store. There are options for both. If you're in that area, you can find rack storage within 10 minutes north or south (up\down San Jose Blvd\rt 13). To the north, you have Goodby's creek. My bud racks his 23' boat there for about $220 a month, but he gets a break because he bought the boat there. It's right by the Hooters. There's also a very nice public ramp on the other side of the road with plenty of parking.
To the south, there's rack storage at Julington Creek. I think the prices there are a touch less. On the other side of the HWY, is a fenced in lot where I see a lot of boats stored on trailers. I'm not sure who runs the joint, but would be happy to find out. I frequent a watering hole right near there. There's another ramp within 2 minutes where you could launch. THere's not nearly as much parking there as there is at Goodby's.
Hope this helps.