I intend to respond to your PM but you've caught me in the middle of a mad scramble to prepare for Solstice and Christmas....
I would search tarmls.com for houses in the central area. I think you'll be hard pressed to find something for 80K that isn't a major fixer upper and it would surely be tiny, which might be OK for you. Here's the Tucson Craigslist
to look at rentals and sales. The neighborhoods are really weird and patchy. I'd say don't go south of 22nd as a general rule. It's really hard to tell though, I would recommend staying a week or so with someone or at a hotel etc. so you can look at the specific neighborhoods to rent or buy in.
We rent and have no hope of buying the near future and we've found we can get a lot more house for our money renting. We rent a 4 bedroom 2 bath house in a great little neighborhood centrally for $1000/month. If I had to bus we definitely could, it wouldn't be my favorite thing but I'm kind of a wimp.
I grew up here and haven't traveled much so I really have nothing to compare it to in terms of the buses. Growing up I bused everywhere, but I haven't done it with kids. This town is quite spread out. For the most part, it's doable, just not easy if you have to walk 10 minutes or more through your neighborhood to get to the bus stop.
The University/downtown area is typically
As for the unschooling group you asked about, we have 2 park days a month plus additional activity days and meet ups. We rotate parks all over town so you might have a tough time busing for that, and the people in the group are really spread out as well. There is the big general homeschooling group that has park day once a week, at a pretty central bus-able park. We are talking about changing it to two park days a week at two different parks and I'd think you could get to either one pretty easily. They also offer tons of other activities.
OK gotta run, let me know if you have other Q's.