In my opinion a 4' x 4' tractor/pen would be way too small for 6-8 birds in Tucson. Even for Cornish crosses. Those birds get big fast - that's why they're raised for meat. For a pen area I usually figure on at least 15 square feet per bird. They need room to get out of the sun and wind and rain and you need to be able to keep their feed dry. People who successfully cram a lot of birds into small tractor pens usually have enough pasture area to move the pen daily. If you don't have room for heritage chickens you probably don't have enough pasture to move a 4'x4' tractor pen to fresh ground every day. It is hard to adequately locate a coop/pen in Tucson - the sun angle varies a lot, wind and rain can come from any direction, and rain is often horizontal. The more space the birds have the more options they have to get out of the elements.
I totally agree with MagicChicken. It is hard to locate a coop here unless you are in a area that has really big, old Eucalyptus or pine trees that can provide a lot of shade and cooling. When I ordered my Cornish cross chicks, the lady at the hatchery asked if I had ever raised them before, and when I said no, she said, well let me give you some pointers. And one of the pointers was, put the feed and water as far away from each other as possible to force them to get up and walk, otherwise, they will just sit there and eat out of the bowl, and drink, never move and have leg problems.
I did as she suggested and had them in a big pen with a walled off corner where they could stay warm (nights were still cold). I did not have any lame ones.
If you want chickens I would definitely avoid Oro Valley. It is the land of the beige, where HOAs rule. Be careful of areas close to Oro Valley, too. The town has a tendency to annex nearby areas. Avoid anything with an HOA. Unfortunately that eliminates most of the housing built in the last 15-20 years.
I like my older neighborhood, built in the 50's, on the NW side (west of I-10). Most of the people who move here want to keep animals and do their own thing without being hassled. It is great that I-10 is very close but driving to Mt. Lemmon is a trek. An hour's drive just to get to the base of the mountain. Might as well drive down to the Santa Ritas or Huachucas to cool off. Not that I'm going anywhere with all my birds
A lot of people west of the Tucson Mts.: Picture Rocks, Sandario Rd area, keep all sorts of critters. Seems like anything goes out there. And the Red Rock area up towards Picacho is getting built up and has farmland. A friend of mine moved up there from near or in Oro Valley. She has goats, chickens, turkeys, not sure what all else. A little bit of a trek out of Tucson, but not too bad. I moved here and rented for a year before purchasing. Gave me a chance to scope out the different areas. A lot has changed since then, that was in 1978.
The city of Tucson is actually pretty good about allowing hens but they don't let you have roosters.
West vs. East Tucson is a preference thing. The west side tends to be less expensive. On the other hand, west side residents tend to wind up driving into the sun when they commute. Folks in the northeast part of town have a lot of traffic to deal with before they get anywhere. A lot of location choices depend on what you will be doing once you are here. Checking it out is a good idea