Jules,
I'm moving back to Tucson in May too. I lived there before, so I already knew which areas are nice.
As a rule of thumb, pretty much anything in Oro Valley will be a safe area. Same for anything north of River Rd. In the near NW, I'd stay north of Ina Rd, and the closer towards the mountains the nicer it is likely to be.
Surprisingly, there are some apartments in the foothills that you can probably get into for around $800, as you mentioned. I used to live in The Arboretum (Kolb near Sunrise), way back when, and it was nice then.
I think the far east side of town ought to be pretty safe and nice too.
Here's a site that has user ratings of apartments. Don't know that I'd trust these ratings that much, but it does have a map of where all the apartments are located, and it has links to the actual apartment pages.
I ended up getting a place in Oro Valley, but there are several way up Kolb and near Sabino Canyon and on Sunrise that you might want to consider.
Really, I'd stay away from south of River Rd, unless you are way to the east.
See this, which you can left mouse click to drag the map to show different areas:
Map results for Tucson Apartments, Tucson, AZ
Here are some results for the east side of town that I found on ForRent dot com
Search Results - ForRent.com
You can pick any area in town and see this stuff. Then, if you find something that looks interesting, maybe you can ask the folks on this forum if they know anything about it. I'm pretty sure you'll be able to find something nice for $800.
Also, some of these places have rental prices in the $800s, some also have move-in specials where the first years rent is, e.g. $780 or something like that (that was true at the place that I found).
Also, on that ForRent site, you can pick your area of town. Personally, I'd look only at Foothills, NW Tucson, Oro Valley, East Tucson (and when looking at the east side, probably further east is better).
Good luck! You're gonna love it.
Oh, and you might want to consider renaming your thread (or start a new one titled) "Need help finding an apartment"