Hey, fuzz, i lived in Tempe for a spell. I managed a cafe in a co-op called Gentle Strength Cooperative. Very vegan friendly there, and great folks.
It's on University Drive, just off of Mill Ave.
You'll become very familiar with Mill Ave.
Every Saturday we had a drum circle on the street, usually starting around 10 or so, and running till 1 to 3 am.
I have a lot of friends on the street there, some homeless, some just spend their time playing music on the sidewalk like I did. I know several vegans and vegetarians there, but unfortunately, having no computers or phones, i have no way to get ahold of a lot of them.
I do talk to five or six though and can tell them to be nice to you.
Also, there's a Whole Foods on Baseline Rd., a little south of Mill, and a Wild Oats somewhere up north near Scottsdale.
It's not a very veggie/organic place in general, other than on Mill, but I'm sure you'll find your way around. Also, Arizona State University borders Mill, so lots of college age kids around, most of them either really cool or else drunk at the bars.
Good Luck! e-mail me for more info!