The Monsoon officially ends this Friday but we are currently getting storms throughout the area. Spring, which can come as early as mid February or as late as April, every years seems to be different, is a gorgeous time of year.
The biggest problem with spring in the high Sonoran desert is the wind and the pollen levels, both of which frequently are off the chart. There are a number of nice state parks available; Catalina, Patagonia or Roper Lakes, Karchner Cavern to name just a few. Some offer W&E and a few have FHU's. There are lots of RV parks to choose from as well.
:C
PS: March through April reservations are a good idea. I agree that the snowbirds begin their north/eastward migration in late March with the bulk of the flock departing by the end of April. This will seriously thin out the RV and State Parks. By Mid May it is getting hot and the snowbirds are long gone.