Krress, I recommend that if your water is bad tasting that you go to one of those water Kiosks that sell R.O water for 1.25/ 5 gallons or go to any store and get purified water. Stay away from distilled water.
If you have the purified water, it has enough minerals to make a good beer. If you have doubts, you can take a PH sample and see how close to neutral the water is. My experience is that if the water tastes good, it will work in beer. Most of the time tap water is just fine.
However, I have heard horror stories about water in Tucson. One of the problems is the use of Chloromine for line disinfectant. That can really kill a yeast growth if it is too high. The only thing that removes Chloromine is Carbon Filters (Activated Charcoal).
Regular Chlorine is sometime used and is very easy to remove by boiling. Back in my old town in Utah I would boil the water, let it sit a night, then use the water.
Let us know what method works for you. I recommend you post on HomeBrewTalk.com - Beer, Wine, Mead, & Cider Brewing Discussion Community.
and it is the sister site to this site. I know BOTH the LBS in Tucson are also great sources of help as far as water goes.
In the end I would bet that if your beer is tasting good, there would be little reason to change the water profile. I have been brewing over 15 years now and I just don't worry about it, but I do live in Sierra Vista and our water supply is pristine as far as city waters go.
Good luck and I hope to see you on HBT.com.