In Arizona, you want to see the Grand Canyon, Sedona, Phoenix and Tucson (old Tucson).
Once all the kids are back in college, you can party in either Tempe (Arizona State University) or Tucson (University of Arizona). Also, if you are over 21 take a quick side trip to Las Vegas for a day or two.
In Florida, visit Orlando, the Everglades, the Space Center (on the coast east of Orlando), Tampa, and Miami. Pick one or more of the amusement parks (Disney parks and Universal parks and Sea World in Orlando, or Busch Gardens in Tampa). Visit an alligator farm near the Everglades and also take an airboat ride. In Miami, go to the South Beach area for clubbing.
Enjoy your trip.
I think you should rethink your plans. Winter, including Christmas, is peak season in Florida. So if your budget is tight, you won't be spending too many days in Florida. The amusement parks -- Disney World, for example -- will be packed during the holidays. Go online and see what the ticket prices are; and you'll be amazed. Hotel rates won't be friendly, too. How will you get around? Will you need to rent a car? If so, it could be expensive. As for Arizona, it can be downright chilly. There might be snow in the higher elevations. You do not want to be in Las Vegas for New Year's. If you're lucky enough to get a room there, the price you pay will be sky high.
I am assuming that when you say Florida you mean South Florida and Orlando area. South Florida is already very expensive as it is and you WILL need money to move around. There is no good public transportation which means that you will most definitely need to rent a car to move around. Orlando is basically all the parks which in December due to the Christmas themes prices rise for park entry. South Beach for clubbing is $$$$$$$ big time, and you will be partying with other tourists as the locals do no go to these places because again, it is $$$$$$. Also, this time is "cold" for us so we will be either hibernating or at work. Also, you will not get to see alligators during December because the waters are cold and they hide in the deep to warm up.
I'm just being honest, I live here and December is just not a good time to visit unless you have family here that can take you around and cover for half of your expenses.
Spring Break and later in April - May would be better to visit.
Arizona I have no clue about, but I think that Las Vegas is more centralized and you may have better luck at finding vacation packages than Florida, we are really spread out here.