I live in Phoenix and I love many things about it. It is not terribly expensive. There is a wide range of prices.
All the places you and Japanfan mentioned are great, and I would add to those - Lake Powell, Tucson (Kartchner caverns state park is awesome), and the North Rim of the Grand Canyon if you have enough time. Also the Petrified Forest national park (Northeast), Chiricahua National monument (southeast)are very good. Bisbee (SE) is an interesting place and on its way you can visit the town of Tombstone, and OK Corral, the site of Wyatt Earp's gun flight.
If you are into native culture, Montezuma castle, which is On the way to Sedona is very good.
My favorite Mexican restaurant in Phoenix is Macayo's. It is a chain, so there are many of those in the valley. I love their salsa. I am not too fond of On the Border. Most Mexican restaurants here are pretty good. You may want to visit Heard museum in Phoenix, to learn about native art.
I would highly recommend visiting the Desert Botanical Garden, particularly if you plan to visit in spring. It is a unique place with cacti that are over a hundred years old and are very very tall.
I have been to Monument Valley just once and it is awesome but I have to disagree with Japanfan that it is better than the Grand Canyon. I have been to the GC a dozen times and never got tired of it. If you have the time, you may want to go to the west rim and see the Skywalk. I plan to go there around the end of April. I have never seen it. Also Hoover dam is worth visiting. It is an engineering marvel.
If you want to see Max Aaron, you may need to go to the Ice Den in Scottsdale. You may even run into Gracie Gold there.
I don't know if there is a turquoise museum here, but you see a lot of turquoise in Bisbee. Also if you go to the arts district in Scottsdale, there are many interesting shops there. You may see a variety of precious stones and other native or Mexican items if that is your interest.
I hope you enjoy your visit to our state.