Hello! I'm a former Windy City res myself - lived in the south 'burbs my whole life and went to Loyola Chicago, then lived in Roger's Park for a bit post-grad before moving to MA and then AZ.
My friend who intoduced me to HB lives in MI, near Traverse City, and there is a very active birth community, lots of farm co-ops, etc. She was also a south suburban girl and now she lives in a house she and her husband built pretty much by hand, has chickens, and is looking into goats!
AZ is HB friendly as well, and we also have all 3 vax exemptions. I have my son in a standard day care, and it was no issue at all. There are plenty of MWs, at least in my area, and more have arrived since I had my #1. There are not a lot of Nurse Midwives though, and I think there is only one birth center and it just opened. Seems like the MI community is more established than the one here, but that might just be my experience - I live out in the boonies and thus don't attend any birth circles which are more Phoenix and suburbs oriented.
No experience with homeschooling, but I have a friend who does.
Biggest upside of AZ - climate. I have to say it was wonderful having a baby that I never had to bundle in more than a fleecy onsie. No digging cars out, or driving through snowstorms! No ice! Summer can be brutal, but fall winter and spring are great.
However, there's no "city". Compared to Chi and Boston, Phoenix (and Scottsdale and Tempe) are sad little baby cities. Museums, theaters, culture... not on the same level.