Knobby,
I last flew with AA in November '99 - seems much more recently than that. I've rented 172s, 152s (inc. Aerobat) and their lovely red Aeronca Champ, and they've about 25 hours of my money!
The aircraft aren't new, and some can be a bit tatty around the edges. In fact they are probably equivalent to a consituent of the average UK club fleet! <img src="wink.gif" border="0"> However, they do the job and the prices (certainly then) were very reasonable indeed. $58/Hobbs hour for the 172, $33/hr for the Champ. Instruction (e.g. for a Biennial) was about $20/hr IIRC.
Take your own headset, and yoke mounted PTT if you're flying the 152s. You can rent them from AA, but if you're doing more than a few hours then your own will probably work out cheaper.
Get a thorough checkout on the effects of Density Altitude. A good hop for this is to Payson, about 30 mins to the NW and at about 5500' elevation. Lovely place, too. The transit will help you with local (and general US) procedures too.
You'll need a US licence, of course. If you don't have one, the place to go is the FAA Flight Standards District Office (FSDO). There isn't one at Falcon Field - I think the nearest is at Scottsdale Muni.
If you're going any distance at all, you'll see a lot of the GABA (Great American Bu**er All), which would be a bit rough if you ended up in it, so a rucksack with water, protective gear and first aid kit - plus a guide to desert survival - tended to help my confidence. Hundreds of outdoors stores can equip you here.
Small list of places to go:
Monument Valley (stage through Page).. .Grand Canyon (of course).. .Meteor Crater (second most impressive big hole in AZ) Winslow is the nearest airfield -Eagles' lyric t-shirts available.
. .London Bridge (Lake Havasu City). .Sedona (airfield in the sky' - on top of a Mesa, and like landing on a rockbound carrier). .+ lots of others. Excellent part of teh world - have fun.