Not all pecans are self-fertilizing ... make sure you don't need to have two varieties. Aside from that, they do well here, as water-guzzling plants.

Almonds do not do very well in Phoenix - as you noticed, the winter chill requirement is a bit high for us.

I have no experience with the walnut.

A mature pecan tree in production needs 6 acre feet of water to thrive. That's a heck of a lot of water and also why successful commercial pecan groves like to flood irrigate. What's that slurping sound?

Wow! I guess I'll keep buying my pecans at the store since I don't have flood irrigation at my house.
Thanks for the info.

Man, I should get some to soak up my excess irrigation! No wonder mine liked the flood area in OK when I lived there!

There are several varieties of nuts that will do well here, if they get enough water of course.

Take a look at Deciduous Fruits and Nuts for the Low Desert, a publication from the University of Arizona. Just click on the "Fruits and Nuts" link from the web address below. Trees that are sold bare root are the least expensive and should be available in December or January.

Here is a link that might be useful: Deciduous Fruits and Nuts

Mahan Pecan is a good choice for low desert. It has a superior quality nut too.
Garden Prince Almond is a good choice and is probably the lowest chill requirement of any almond. Since it is a natural dwarf, it will be a good back yard tree too. But don't let that fool you, it's still a good size tree like a peach.
Walnut is the hardest one for the desert. Pedro would be the one to try. Excellent nut and it's said to need only 400 hours chill, which is still a stretch but maybe. It's also a naturaly smaller Walnut, so good for yards.

I did pick up Garden Prince Almond trees at Lowes the other day at 1/2 price since the leaves were a bit browned around the edges. Hopefully, I can keep them at around 8 to 10 feet in size. Now that it has cooled down, I will be planting them in the next couple of days.
There is a low area that runs parallel to a small wash in our yard and I plan on putting these 2 along with some dwarf cherry trees in this area hoping to get a little more chill hours.

Hey Agility_Mom, how did it go with the Garden Prince Almonds? Did you keep them 8 to 10 feet? Are they getting enough chill hours?

Yes they did get enough chill hours, I got almonds (although not a lot) one season but I had a big tree fall over in a storm that crushed them.
They were easy to keep pruned to size while I had them.
So, I just planted another Garden Prince in a different location as well as an All-in-one.