OT: Former ASU shooting guard Evan Gordon transfers to Indiana

Lots of options and without knowing your style preferences, hard to make recommendations, but some of my favorites in your general area:

• Chompie's (near intersection of Rural and University):  It's a combination of a jewish deli and a Denny's.  This is the place to go when you are starving.  It's not a trendy place, but it get's the job done.
• La Bocca (on Mill Avenue):  Unique, tasty flatbread style pizzas, unusual toppings, amazing pitchers of sangria (no, not quite Dominick's level).  Good date spot. 
• Morning Glory at the Farm at South Mountain (Southern/32nd street):  This one you'll need a car for, but before your internship ends you have to have breakfast at this place.  Awesome food in a really unique farm environment.  If you have a dog, bring it, you won't be the only one.  Let me recommend the french toast, but anything you order will be fresh and totally out of this world.  Outdoor seating only and they close for summer months. 
• Rula Bula (Mill Avenue):  Irish-style pub, good, lively crowd, decent prices.  Of the Mill Ave bars, this is my fave.

Good luck with the upcoming summer!  I've been here 7+ years now and it's not bad anymore, but that first one was some kind of awful.  Hydrate. 

For food in Tempe, Four Peaks, Oregano's, Tott's Asian Diner, Ted's Hot dogs and Nello's are a must.  For bars, I'm partial to the Vine on Apache (it's dumpy, but I loved it), as well as Mac's Broiler Room and Tap on McClintock and Guadalupe, and Papago Brewing (they sell Bell's) on Scottsdale and McDowell

I only tried the Dilly's Deli on University, and as a NY Jewish deli snob, there wasn't nearly enough meat for me. 

I went to ASU for grad school and spent way too many years there...wasn't a big fan. My favorite thing about living in Tempe (and the entire phx area) was getting the hell out of there. Drive 1.5 hrs in any direction and you'll be in mountainous wilderness. So many amazing spots where you could backpack in for 2-5 miles and find a gorgeous creek or swimming hole with nobody within miles of you. 

As for favorite places: mine were Casey Moore's (hipster bar), Sail Inn (hippie bar, great bands from time to time), Yucca Tap Room (rockabilly dive bar with shuffleboard), 4 Peaks (great bar food, some really good beers), Papago Brewing Co (great beers, pissed at them for replacing the old school juke box with an internet based one). I avoided Mill Ave like the plague because it was full of tourists, bro dogs, and sorostitutes, but so is the entire phx area.