It doesn't get much easier than Desert Wells. I haven't explored San Tan much but I believe there's only one road through there (Brenner Pass) and it's not all much fun. That still dumps you out there to the other side of San Tan which is all rez. No go through any of those parts.
The place I was talking about out there in Johnson Ranch is here
. It's a pretty neat area and it seems like the fences go up and as soon as they do, a week later, they go down.
So it may be worth a shot to go out there an poke around. Here's a pic from last time I was out there with the kid.
I may be going out this weekend with the kid just to put put around. Maybe we can get a super n00b ride goin'.
ps. you may just want to find an empty lot nearby and get your feet wet that way. I had luck at both places I've lived (val vista & pecos) and here in Queen Creek that I've found empty areas that nobody really seems to give a fuck about and I go out there and do some pop a wheelies and donuts when I get a dirt low.