OK...here's the scoop on Tucson. (I have a place there so I know a thing or two about the place).
In Tucson you have the "flats" and you have the foothills. The University and the stadium are just east of downtown, down in the flats. Not the nicest part of town. Not "scary" really, just nothing very nice.
In the foothills (north, northwest and west) are nicer hotels, all of the upscale resorts, etc. Much nicer neighborhoods, more scenic as you have some views, but probably a little pricier as well. It's not prime-time tourist season in September so there should be some good deals for the taking.
Any other questions I can help with, let me know.
PS...My place is in Oro Valley (north) give to give you an idea.