We've been out there every year since 2009 for ST, twice with our 5th wheel, and like it so well we've now bought a home. Depending on when you are planning to visit in March you shouldn't have a problem. Particularly later in the month many of the snowbirds are returning north. I guess where you stay somewhat depends on what team you're going to see, but all the stadiums are within an hour of each other. If you don't need sewer, on the east side of Phoenix I'd suggest Lost Dutchman State Park in Apache Junction (site 32 is a beautiful pull thru), Usery Mountain Regional Park in Mesa (our signature pic is from here), or Cave Creek Regional Park in Cave Creek (latter two are county parks). All 3 are beautiful and I think a better experience than the typical snowbird park. On the west side we've only stayed at Leaf Verde RV Resort in Buckeye. It's nice, but is a typical snowbird park. I see you're from Colorado, so I assume you'd like to see the Rockies. They train in Scottsdale (beautiful stadium, probably nicest one out there), so any of the locations on the east side would work, with Cave Creek probably being the closest. Incidentally, the Rockies do regularly sell out, so get your tickets ahead of time. You'll also need reservations at the state and county parks, and it's not too early to make them.
If you let me know your interests and time constraints I'll be happy to suggest some other things to see. Incidentally, While Tucson is nice, there are no longer any teams that train there.
2013 Columbus 320RS
2013 Ram Laramie Longhorn 3500 Dually 6.7 Cummins
Days Camped 2013 - 50