PIZZA:

• Spinato's - Thinner crust pizza with a somewhat sweet sauce.  Multiple locations.  Probably my favorite pizza in AZ. 
• Pizzeria Bianco - regarded as the best pizza in AZ and possibly even the country.  Neapolitan pizza with local fresh ingredients. Try the location near the Biltmore in Phoenix for less crowds.
• Cibo Pizza - Downtown Phoenix. Neapolitan pizza.  Also very good.  A good alternative to Pizzeria Bianco.
• La Piazza Al Forno -  Neapolitan pizza located in Downtown Glendale closer to the stadium.  Easily the best restaurant in relative close proximity to the stadium.
• Federal Pizza - In uptown Phoenix. I have never been here but I've heard good things. The place is owned by a local restaurant group (Upward Projects) who almost always hits it out of th epark with all of the restaurant offerings (see Windsor below for burgers).
• La Grande Orange Pizzeria - One of my favorite places. Located in Arcadia. Also started and operated by another local and extremely successful restaurnat group (LGO Hospitality).   
• Nello's Pizza - Multiple locations. Skip Lou Malnati's and go to Nello's for authentic Chicago-style deep dish pizza.
• Barro's Pizza - Cheaper option but my go-to place for the family. I've been eating Barro's since Day 1 and I still love it.  Locations throughout the Valley.

BURGERS:

• Zinburger - Great burgers and milkshakes. Located at the Biltmore and in Gilbert. Not cheap for a burger. Try the Breakfast burger and the green chilli fries.
• Rehab Burger Therapy - Large burgers on Pretzel bun.  Located in Old Town Scottsdale (new location off of Mill Ave. is not yet open). 
• Shake Shack - Yes, this is a chain but I like their burgers better than almost anywhere else. Located in Scottsdale Fashion Mall and in Uptown Phoenix.
• The Stand Burgers and Tacos - Located in East Phoenix in a small building.  Great burgers, better milkshakes. 
• Windsor - Located in Uptown Phoenix. One of the best burgers I have had.  Don't get the Windsor style, get the Classic style. 
• Chuckbox - Located in Tempe right by ASU. Not the best burger but this place is an institution. It's a dive and it's good. 

There are other places ot get more fancy burgers (i.e., Relish Burger Bistro, Roaring Fork, Grassroots Kitchen & Tap, Zinc Bistro, Delux, etc.), but the above places are my favorites becxause they are more classic and not all high-brow. 

MEXICAN:

This one is hard because everybody has different opinions.  But here is my list:

• El Bravo - North Central Phoenix.  My favorite Mexican place in town.  The green corn chicken tamale is probably my favorte Mexican dish in AZ.  It's been around forever and it is very good.  
• Barrio Cafe - Phoenix. Consistently ranked as one of the best restaurants in Arizona. Very good Mexican food that is a little more than just tacos and burritos.  Highly recommended.
• Mango's - Downtown Mesa. This place is run by the De La Cruz family (who also runs El Sol and El Zocalo in Chandler and Phoenix Burrito House in Phoenix).  I really like this place and it has been one of my go-to Mexican places for about 20 years.  The Killer Burrito is good as are the beef tacos.  
• Rancho de Tia Rosa - Gilbert. Some people swear by this place. It is good but I don't rate it as high as other people do.

I'm going to stop here because this list could go on forever and everybody could list 10 different places.  The places above are 3 of my favorites with Tia Rosa's thrown in because so many other people love it. 

BEST OF THE REST (IMO and off-the-top-of-my-head):

• Steak 44 - Phoenix.  Expensive ($$$$).  Probably my 1a favorite restaurant in town right now. 
• Mastro's City Hall Steakhouse - Scottsdale.  Expensive ($$$$).  Probably my 1b favorite restaurant in town right now.
• Donovan's Steakhouse - Phoenix.  Expensive ($$$$).  Very good steakhouse.  More mahogany and classical.  Consistently fantastic.
• Little Miss BBQ - Phoenix just south of the airport. Probably the most popular and acclaimed place in town right now.  If you can brave the line, the fatty brisket is the best I've ever had.  Save room for the small pecan pie too.
• Binkley's, FnB, The Mission, Citizen Public House, Cowboy Ciao, Sushi Roku, Mastro's Ocean Club, Noca, St. Francis, The Henry, Pomo Pizzeria, Joe's BBQ, Joe's Farm Grill, Liberty Market, Oregano's (sorry Kimchi), Portillo's, Coconut's Fish Cafe, The Vig, etc., etc., etc.

I've mentioned above about a few restaurant groups.  In the Phoenix area, there are a few restaurateurs that are extremely successful and you really cannot go wrong with any of their offerings.  You will have a good experience at any place owned and operated by the following groups or people:

• Upward Projects
• Fox Restaurant Concepts
• Joe Johnston
• LGO Hospitality

I could list a lot more places, but I have to stop somewhere. 

One interesting thing to note ... Sky Harbor Airport has BY FAR the best restaurant options compared to any other airport.  All of the best local places in the Phoenix area have a place in the airport.  If you see a restaurant (sans Chilli's) in the airport, you can to their main location in town and have a great meal.  (BTW, there is a place called Modern Burger in Terminal 4, I think at the B gates (American Airlines).  It is the best burger in town. It used to be a part of a Fox Restaurant called Modern Steak at Scottsdale Fashion Mall.  Modern Steak was my favorite steak place but it closed (Shake Shack is now in that location).  But Modern Burger remains in the airport and it is great.)

Happy eating!!!