Utah is a great Idea and march is perfect. Moab isnt the best place for backpacking because of all the mtn bikers. Your closest bet would be Canyonlands. The needles district is really pretty. You have so many options it ridiculous. Trachyte creek area is cool, Robbers Roost area when Arron Ralston cut his arm off. My favorite area is Canyons of the Escalante. Check out Death hollow. Its a good 3 day trip and extremely impressive. If you are looking for long there are all kinds of multiday loops in the in the Escalante. Stay out of Zion. Its more of a day hiking area. The Barracks which is near Zion is pretty incredible too. Utah is limitless. Depending on where you go in Southern Utah the best flight options are Grand Junction Co, Flagstaff, Las Vegas. Cedar city and St George. SLC is a bit of a haul from southern utah. BTW Toas is in NM, Not AZ

If you decide on going to utah private message me. I can give you some good idea. I have spend more time than most in Southern utah and know it like the back of my hand. I have maps already made and gps coordinates and some awesome loops