Most of the more desirable state and county parks will already be booked up, you can however get into the overflow areas in the ones that have them, and save a few bucks too. Dead Horse Ranch is worth a couple weeks, had friends stay in the overflow. Usery and McDowell were worth the week in each we've stayed. I heard Lake Pleasant is too although I've not stayed there. Gilbert Ray is 1st come 1st served, we had no problem getting in showing up when they allow check in. Catalina SP was excellent, as was Lost Dutchman, they'll be full as may be the overflow, worth a try though.
Organ Pipe was real noice, also first come first serve. You'll see a bunch of folks boondocking just before you get there so that's an option too.
A few other spots, Kartchner, Patagonia Lake, and our favorite, Bonita in Chiricahua Nat Monument.
Coming from the east on 10, we like a couple nights in City Of Rocks SP in NM, mostly FCFS, but you need to pull in pretty early, not many sites can handle a bigger trailer rig. We've been finding it's too cold coming in on 40.
If you go that route, Balmorhea, Seminole Canyon, and Davis Mountain SP's in TX are nice. Seminole's dry area is worth using. They were rebuilding Balmorhea last winter so you'd have to call ahead.
