Hey Garry -
You probably won't be able to venture into the San Juans much due to the abundance of snow still around in late May. Although, you may get in some good snow climbs if you start early before daily melting begins and avy danger increases. I wouldn't go alone, though, if you are unfamiliar with the area.
Black Canyon is astounding. If I ever go back, I would take a couple days and get down to the river level itself, not just look down from above. There are a lot of little jaunts that give you interesting viewpoints all around the National Park.
If the snow permits, you can do some nice 2-3 day loops in/around the West Needle Mountains, just across the road from Durango Ski Resort. Getting down to the Animas River is beautiful in and of itself, without having to go up into the higher peaks. IIRC, most of the loop hikes going to/from Highway 550 and the Animas stay below 10,000 feet, so snow shouldn't be too much of a problem in late May.
Trails Illustrated map #140 is your best bet. #141 would be good to have, too.
There are also some good day hikes out of Telluride and Ouray that I think would be appropriate in late May, although I'm not as familiar with those.