Old-town Scottsdale is worth a wander around, and you can do so before going to a game at the stadium. I'd also take in the Body Worlds exhibition at the Science Center; I saw it back in 2002 in London, and it was fascinatingly creepy. Or maybe creepily fascinating, I'm not sure. ;-) We always take overseas visitors to Rawhide, and feed them deep-fried rattlesnake, but if you're from Texas, you probably have had your share of pseudo-Western kitsch!

Tucson, I've only ever been to for baseball, wrestling and the Gem Show, so I can't really comment on its delights. It seems, if anything, to have less to offer than Phoenix, but hopefully a local will provide more useful info. Traffic in Phoenix is generally not bad, given the size of the city, but rush-hour can certainly get a bit messy, and is best avoided if possible.

With regard to getting autographs, I believe it may be easier at the practice sessions, than before a game. Here's the info on those. If I think of anything else, I'll add it: hopefully others will chip in with hints and tips too.