I'm restoring an 86 samurai that has been sitting in the desert the last 10-15 years. I was wondering if there were any places I should look specifically for rust. Also, what are some of the other things I should check?

The most common rust places I know of are around the wiper arms and in the wheel wells.

If it's been abandoned that long,
Find out Why?
Check for major structural damage, Bent... frame, Spring mounts, axles,etc.

Also, Carefully, see who moved in!!!
On a rusty iron rescue mission with a buddy of mine,
half way back to his place, a Bull Snake came crawling out of the head liner!!!
I though that something came apart in the steering when I was following in the "Chase Car"!!

CAPT

LOL, I had a rabbit come flopping out of the hood of an old Caddy
I popped the hood on looking for good junked cars to sell

My parents have actually been the only owners. The transmission went out while the vehicle was loaned to a family friend, and it has been in his yard since.