Before we talk about Tucson, I want to make sure you know that Phoenix/Scottsdale will be warmer than Tucson, in March and pretty much every other time of the year. Has to do with elevation more than north/south distinction. Sorry if you already knew this, don't mean to sound rude, it's just when you said South Arizona--for some reason Southern Arizona is more common--I wondered.

NewbE - Thanks for that info. I actually didnt know that. Havent explored that side of the country much. Any suggestions on what are the things to do in and around Scottsdale/Phoenix? Thanks.

NewbE - Also I checked the weather for Tucson, and it looks like it averages around 60-65 in the days and 40-45 in the nights. We are ok with this weather as we'll get to see a new place and will not have to repeat Florida

Hi, Rs--
Have you been to Sedona? The red rocks are gorgeous!
In and around Phoenix, there's the Heard Museum, the Frank Lloyd Wright compound Taliesin West, lots of golf, the Desert Botanical Garden... You could also divide your time between Phoenix and Tucson as they're only 3 hours apart and an easy drive at that.

You beat me to it! You're right, Tucson won't be cold, and the warm sun will be out
In and around Tucson, my favorite thing to do is the Arizona-Sonora Desert Museum, which is kind of like a zoo and a botanical garden in one. Saguaro National Monument has an interesting visitor center and some very easy trails. Not far outside town, Mission San Xavier Del Bac is lovely to visit; if you're into caves, there's Kartchner Caverns. And about an hour and a half from Tucson is the mining town of Bisbee, very historic and picturesque, where you can tour the old Copper Queen Mine. There is also spectacular birding south of Tucson in the Huachuca Mountains, if that interests you.

Tucson and Phoenix are 1 and a half hours apart driving on I-10.
Things to see: Arizona-Sonora Desert Museum, Sabino Canyon, Mission San Xavier del Bac, Mt. Lemmon drive, University of AZ, Gallery in the Sun, Pima Air and Space Museum, Kitt Peak Observatory.
Museums include several at the U of A, including Photography where Anson Adams gave his collection.
Much less traffic in Tucson than Phoenix area. Day trip south to Tubac and Tumacacori. Nogales, Sonora
60 miles south.

You might want to think out of the Arizona box and consider Palm Springs, CA. It's in the Sonoran desert like Tucson and Phoenix. It's in CA just because of where the state line has been drawn. Average high in March is 79F vs 73F for Tucson. (http://www.weatherbase.com/)

Long time winter escape for celebrities from the east. Plenty to do in the adjacent LA basin. (Big understatement). Example: about 1:40 to Disneyland.

In the Palm Springs area:
http://www.palmsprings.com/attractions/

Disclaimer: I haven't been there for years and live 3+ hours away.

Last Saturday and Sunday I was in Yuma. It was a bit chilly in the mornings Sunday and Monday but warmed up nicely by noon.
Monday I drove from Yuma to Gila Bend and then south into the Organ Pipe Cactus NM. If I had had my passport with me I might have got the Mexican car insurance and gone to Puerto Penasco.
The cheapest gas that I saw anywhere was in Tucson ($3.149).
I spent the night in Coolidge east of Phoenix and there was frost on my rear window in the morning.
Maybe it will be a little warmer in March.

My son's birthday is in the middle of March. We would always have outdoor birthday parties for him when we lived in Tucson because the westher was so lovely in March. The high temperature was typically in the 70s that time of year though it cools off at night in the desert.

I would choose one location for that amount of time instead of driving between Tucson and Phoenix.

In Tucson I recommend Saguaro National Park, Catalina State Park, Sabino Canyon, the Arizona Sonora Desert Museum and Mount Lemmon. Nice places elsewhere in southern Arizona include Bisbee and the Chiricahuas. It will be chilly in the mountains.

I did not spend that much time in Phoenix so cannot help there. It typically is about 5-7 degrees warmer than Tucson.

Hope you have a great time.

Sedona can have snow in March.

If you need ideas for Tucson and Southern Arizona, please check my blog and click on the links:

http://mikepintucson.blogspot.com/

If you enjoy wine tasting there are quite a few wineries just south of Tucson.