You have a car? Stop by Idaho Springs along the way and have lunch. No to Garden etc. 'way 'way out of the way, so to speak.

If you leave Breck very early, 6-7AM, you could drive through Rocky Mt Natl Park, have lunch in Grand Lake and be at the airport in plenty of time. Spectacular scenery. Or, go to Georgetown, have breakfast at The Happy Cooker and take the train trip and mine tour. Idaho Springs is interesting but doesn't take long - just a drive or walk along a main st. If you go there, have lunch at Beau Jo's Pizza. You could go through Golden after that and do the Coors Brewery tour.

Since Colorado Springs (Garden of the Gods) is about 100 miles from Breckenridge and the Denver airport 75 miles from there and since Grand Lake (west entrance to the RMNP) is about 100 miles from Breckenridge, then thirty miles through the Park to Estes Park then about 75 miles to the airport, I agree with irishswampyyankee's suggestion to go to Georgetown and ride the train, and walk around the town. But if you want something closer to Denver and would like see some more red rocks, Red Rocks Amphitheater is just off I 70 west of Denver--This is where concerts are held in the summer. There is also a photo gallery featuring many of the performers who have played there--a mini rock and roll hall of fame. http://www.redrocksonline.com/

Or if you want to go into Denver, there is the Art Museum http://denverartmuseum.org/home, Botanic Gardens http://www.botanicgardens.org, Museum of Nature and Science http://www.dmns.org/, the Zoo http://www.denverzoo.org/ There are lots of casual restaurants in Denver. Two of our favorites are Racines http://www.racinesrestaurant.com/ and Steubens http://www.steubens.com/

I'm not that impressed with Idaho Springs, perhaps because I've been through there so many times. There's certainly little there to keep you busy for more than an hour or two.

The Georgetown Loop Train is a good idea. Another possibilty is to get off I 70 just past Idaho Springs and take Highway 6 toward Golden. It's a very scenic drive. You might then head up to Boulder ( highway 93) and the Pearl Street Mall, lots of different shops, street entertainers, pubs and restaurants. You could also do a short walk along Boulder Creek. The E 470 makes for a fairly quick trip to DIA.

Don't forget that Denver has a lot to offer too.

We enjoyed exploring historic Georgetown even w/o the railroad ride

In Golden, Lookout Mt and the CO Railway museum are other options

TommyKnockers restaurant in Idaho Springs has specialty beers, fabulous root beer and great burgers. Then take Colorado SH103 to Echo Lake at base of Mt Evans. You can drive to the top ($) or not, then continue East/South on CO SH103 to CO SH74, turn left onto SH74, and travel @ 3mi back to I-70. This is a pretty loop that gets you off I-70 for some pretty views of the Front Range.

Or the Denver Art Museum. The Denver Mint. The Denver Zoo.
Denver food: The Buckhorn Exchange. All sorts of stuffed critters and old celebrity photos. Buffalo,rattlesnake, and mountain oysters still on the menu. A truly old place (late 1800's)still open and still in the same place. The normal food is quite good. A genuine curiosity.

Thank you everyone for these great responses! I will report back soon.