Of the places you listed, Bryce/Zion is your best bet. Early May is a great time and there are timeshares in St George which is a good base.
The other places are better in September after Labor Day if you want to do some hiking. May and early June is a great time to spot critters and their young.
This year, there wasn't much snow so hiking was a month earlier than normal. I was in the Canadian Rockies the first week of June and quite a few trails were open along with the grizzlies being awake and active with their young. As a result, we stayed with the popular trails and made sure we had lots of company. In a normal year, the only hikes snow free would be very low elevation for only a short distance. I was there in a normal snow year the 2nd week of June and there were so many bears with their young out making up for a hungry winter that it didn't feel safe to hike anyplace. However, we saw lots and lots of critters and babies and it was a fantastic trip. It really depends on what you want to do.
This year is forecasted to be a strong El Nino which usually means warmer and drier in the NW and wetter in the south. So more snow in Colorado and California and less in Glacier and Canada and maybe Yellowstone.
Besides the big National Parks, take a look at the smaller National Historic Parks or N Monuments. There are a bunch of them around Sante Fe which would be great in May. To find these hidden gems, go to nps.gov and select find a park and then pick whatever state you want. A list of the various locations will come up and you can click to find out more info.
http://www.nps.gov/state/nm/index.htm . One of my favorite small parks is El Morro in western NM which we did as a stop on the way from AZ to Sante Fe. There's a rock face above a spring that is soft enough to write in so travelers over the centuries have left their marks. The stories are fascinating and there's a beautiful hike up and over the rock.
Sue
