Statistics like the ones you're asking for tend to be hard to come by because different states have different rules for homeschoolers. Some keep very extensive records; others keep basically none at all. Most of the statistics I've read claim only to be estimates, and they tend to vary wildly depending on who is estimating and what they're arguing. Pretty much everyone agrees that homeschooling is on the rise.
You can look at the homeschooling laws for each state. Ones that are more homeschooling-friendly tend to have more active homeschooling communities, I think. Of course, do an online search for homeschool groups, and if you see lots or big ones or inclusive/secular groups, it's more likely to be a vibrant homeschooling community. If there are few groups or they're all religious, then it might not be the place for you.
We live in an area that seems very homeschooling-friendly. I'm not sure homeschooling is quite mainstream, but it's close! There are at least 2 LARGE (over 100 families, and maybe closer to 200) secular/inclusive homeschooling groups here, plus a secular local online group that shares resources. I'm sure there's overlap between them, but still! We also have a school for homeschoolers, complete with a yearbook and afterschool groups for things like drama, chess and knitting. It's very handy! No sports teams yet, but the place is growing...
Based on what I see in my area, I'd recommend looking for a town with lots of schooling options--lots of private schools in a variety of forms (religious, secular, college prep, etc.)--since that would probably indicate either some dissatisfaction with the public schools (and thus a willingness to try other things) or a tradition of independent thinking. If everyone is at the public schools or one other (probably religious) private school, you'll probably encounter resistance.
A strong public library system and a busy parks system with daytime classes for kids would also tend to indicate homeschoolers in attendance. Arts centers with daytime classes are another indicator. You could find all these things online, I think, if you have a specific place in mind.
Another thought is to look for places close to the Mason-Dixon line. This is a gross generalization, of course, but it seems like there you get a combination of the religious homeschoolers loosening up expectations and a more northern secular focus, too. Our town is fairly close to the line, and that's what I see here.
HTH! I'm happy to discuss further if it helps.
