I love the Phoenix-Scottsdale area! Some nice things to do: 

The Heard Museum is a great museum about the native tribes of Arizona. I loved their exhibits, and catch a free guided tour if you can. They also have native dances and other cultural events throughout the year.

The Desert Botanical Garden is pretty cool, different from any Botanical Garden you've seen, with all the different species of cacti and desert plants you can find in the State. When we went they had a nice Chihuly glass exhibit scattered among the plants. 

Go to the top of South Mountain Park take in the view of the valley. You can drive to the top or you can hike. 

I love the  Taliesin West house, designed by Frank Lloyd Wright, in Scottsdale. You can go on a guided tour during the day or night and learn more about one of the most famous houses designed by FLW.

I also enjoyed going on a hot air balloon ride in Scottsdale, there are a few companies doing it at sunrise and sunset. You finish it off with breakfast or happy hour at whatever location the balloon lands. 

For food, the famous  Pizzeria Bianco is one of the top in the country, and I was impressed by the menu at  Nobuo at Teeter House, a japanese place right across the street. Both are located at  Historic Heritage Square.

In Tucson,  Lindy's Diner On 4th is a fantastic burger place. I always get the Mac & Cheese burger. 

In Phoenix, there's a lot of great places to go. Be sure to stop at  Lo-Lo's Chicken & Waffles for some good Southern food.  Mrs. White's Golden Rule is in the same family and fantastic for soul food. (Yes, there's a difference.)

Welcome Diner has a great patio and is perfect for cajun food and drinks. Up in Scottsdale  Grassroots Kitchen & Tap is a little on the nicer side. You can't miss the pizza cookies at  Oregano's Pizza Bistro either.

For the bar scene,  Angels Trumpet Ale House and  The Vig are great spots Downtown. In Tempe, you can find a range of bars - if you don't mind college students around. If you'd like an older crowd, head to Scottsdale. 

Go hiking at  Camelback Mountain and if you have time for a two-hour drive, head up to  Sedona. There's a ton of hiking and the drive from  Phoenix is incredible. 

In Phoenix, you should get a Sonoran hot dog at Nogales Hot Dogs. It's a bacon-wrapped hot dog loaded with beans, onions tomatoes, guacamole and cheese.  I also like Italian Restaurant. The generic name doesn't give give justice to the amazing food coming out of the kitchen.  If you find yourself a little up north, you should go to Rock Springs Cafe. Order the mesquite-smoked pork ribs, and for dessert their famous Jack Daniel's pecan pie.

In Tucson, you should check out Taqueria Pico De Gallo. I loved the menudo made with beef tripe, tendons and hominy.

By the way, if you're around for the Arizona State Fair, go. Fantastic fair foods from batter-fried bacon dipped in sausage gravy to Navajo fry bread filled with mutton stew to batter-fried peaches.

You've got a try the Mexican food at this historic award-winning family owned restaurant named El Bravo. They've been acknowledged as a best of best in Phoenix many times, especially for their green corn tamales with chili and cheese. Definitely a must visit as long as you don't mind a laid-back casual environment.

Andrew Zimmern gave you some great suggestions. Just a few more to add - (If you're looking for fancy, ignore me.)

Chino Bandido (2 locations I think) Complete dive but delicious food. Greasy mexican/chinese food. 15+ different meats that you can order plain, in a burrito or in a quesadilla. Ask for help! They know it's confusing and there are lots of options so they offer help and samples. My favorites - Jade red chicken, black beans and jerk fried rice. 
Carolina's Mexican Food (3 locations) Started as a single location downtown. All the cops, firefighters and city workers got lunch here. Good mexican food. 

Lots of great places to hike around town if that's your thing. Oak Creek Canyon/Sedona is beautiful but an hour or 2 in the opposite direction. 

Pizzeria Bianco is a great pizza place but waiting for dinner can be a pain - if you want to go and avoid the people go at lunch

Four Peaks Brewing Company is great

El Charro Cafe is good if you need mexican food in tucson

The Phoenix area has some of the best Mexican food to be found:  Macayo's Mexican Table, Carlos O'Brien's Mexican Restaurant, Aunt Chiladas Squaw Peak... if you like burgers, Bourbon Jackshas great ones (Scottsdale Rd. & Mayo Blvd.) Many other ethnic eating opportunities to be found, too.

Hiking is good around here, and someone already mentioned Sedona... gorgeous area with good hikes all over.  Between Phoenix & Tucson is Picacho Peak, which has a good hike to the top. (regarding hiking in this area... take lots more water than you think you'll need)

Cave Creek/Carefree is a nice area to explore.  Good restaurants there, too.

The Lobby Grill at Arizona Grand Resort has really good pizzas and burgers. Just thinking about them makes me want to book a plane ticket to go back to Phoenix :)

Unless you are into discount malls, there is nothing really to see between Phoenix and Tucson.  In downtown Tucson by city hall is the old cathedral, which is worth seeing, and the art museum, which is, too.  And just down a couple of blocks on Church street is one of the finest Mexican restaurants in town, El Charro Cafe.  There are a lot of things to see and do in Phoenix/Scottsdale, most listed in our various tourist websites, and which your parents will know, too.