The Denver art museum just unveiled its large expansion designed by Daniel Leibskind in downtown Denver. The building has gotten some mixed reviews, but it's going to be worth a visit.
Boulder can be pretty busy around graduation time. A "classic" Boulder activity would be to go to dinner or weekend brunch at Chautauqua. It's right in the foothills-has the view down the meadow. The restaurant varies between really good and adequate but is in a cool old building left from the Chautauqua colony. It's often very busy.
If you're into weather, you can tour NCAR. It's in an I.M Pei building that looks out over the valley to the east-great views and interesting exhibits-and free. There are often deer wandering around in the valley below.
http://www.eo.ucar.edu/visit/
Also, Rocky Mountain National Park is an easy and very scenic drive, about 40 miles from Boulder. There's a road through the whole park called Trail Ridge road. It gets to about 12k feet at the highest point, so you won't want to go there the first day you're in town-definitely wait to get acclimated first. Even if you don't drive all the way through, it's a beautiful park full of elk and other wildlife. Estes Park, the town outside the park is very touristy, but still scenic and probably worth a wander or a stop for lunch.
A really easy but also scenic drive from Boulder is up Boulder Canyon to Nederland. Nederland is kind of funky...has a bit of a hippie reputation, but the drive to it is pretty.
Both Denver and Boulder have pedestrian shopping malls. I prefer Boulder's. There are often performers on the weekends and the people watching is good. There are some nice shops and a good assortment of restaurants from nice and upscale to cheap and semi-scruffy.
It's usually easy to get tickets to Rockies baseball games, but if it's windy the seats near the edges and top can get really chilly.
If you've got the time on your return from Vail, take the return trip from Vail over Loveland Pass, Hwy 6. Very scenic and mountain-y and steep.
Georgetown is a cute, quaint little town that's just off I-70 on the way to/from Vail. It's a very small town, but has some very nice old Victorian houses. They also have a steam train during the summer.
You might want to tour the Red Rocks amphitheater, which is just west of Denver and has nice views. (GREAT place to go to a concert, too, if there's anything playing when you're there)
Denver Museum of Natural Science is very good and in an area right near the Botanical garden and zoo. The botanical garden is really well done.
One thing-the weather in May can be unpredictable. It can be nice and warm or chilly. It can even snow, although it melts off very fast. Plan for versatility in your clothes.