Don't know if you will be spending all your time around Tucson as I am not real familiar with southern AZ rides, but the ride up Mt. Lemon is awesome. Just make sure temp's are well above freezing up top as I saw a post by a Vision rider that lost it on black ice. If you are staying in Tucson, might want to check out Kitt Peak if you are interested in astronomy. They have the largest telescope facility in the country.
Another nice ride would be to take the back roads from Tucson up to Superior, then up to Globe. If you have time, ride an hour north of Globe to Salt River Canyon, it is awesome!
If you spend a day around Phoenix, another good ride is from Scottsdale to Payson, then over to Camp Verde & back to Phoenix via I-17.
Either way, I am sure you will enjoy the Grand Canyon state. I am looking forward to some warmer weather & March is usually in the 80's in the desert.....hard to beat!
Good luck & stay safe!
"THERE IS NO SUBSTITUTE FOR VICTORY" General Douglas MacArthur