A week in Denver!!

I had the good fortune of being invited by a professor to a conference in Denver next week and was able to push back my flight home to give me an extra 8 days there. A couple days will be spent seeing family and friends but I've got a bit of time set aside to hike and climb. I was thinking of doing a 3 day backpacking trip and two days doing some sport climbing(I'm leaving most of the trad gear at home). Can anyone reccomend a good 30-40 mile loop that packs in a bunch of really stellar hikes/vistas. Could someone suggest a good crag with a short approach so I can maximize my climbing time?  Looking to climb sport routes in the 5.10-11 range

Any and all recommendations and advice is appreciated. 

CCC for the sport climbs. The Mt Evans, James Peak, or Lost Creek Wilderness areas, or RMNP, for the hikes.

Lost Creek is probably the largest area; you could even do inner SPlatte/Sheeprock for some climbs.

Little Eiger in Clear Creek should be good for short approach and lots of 5.10-5.11. It also gets shade for most of the day.

Do you want to stay close to Denver for your hiking trip?

The Flat Tops Wilderness for your hiking and back-country. The Devils Breezeway up there is a must do.

I have a good list of backpacking trips i've taken in the area. PM me if you want specific details.