Short answer: go to Rifle. Based on your posts here and over at RCTM, I'm assuming that you're looking for sport climbing at ~5.12. Rifle is the best place in CO (and USA in general) for this in the summer. Although they have had a very wet/seepy spring, it should hopefully be dried out by then. The climbing and camping are both excellent, and partners are extremely easy to find. You need a car to get there, unless you can find someone in Denver to go out there with. Flying out a week early and getting a rental car would absolutely be worth it. A week should be enough time to get a taste of the place and adapt (somewhat...) to the style there; I wouldn't recommend less than a week.
To answer some of your other questions:
Jon Frisby wrote: 1) is it easy to get from DIA to any decent climbing area without a car?
Easy? Not really. Possible? Yes. You could catch a bus to Boulder, and then there are various climbing options within walking distance of town, plus you could likely troll for partners on this site to drive from Boulder to other crags. Still, this might be a hassle. Plus, you can't camp easily near Boulder, so you'd need to find someone's couch to sleep on, or shell out for a hotel. In that case, you'd be better off just getting a rental car; this would definitely be worth it and open up a lot more options.
Jon Frisby wrote: 2) Where is the easiest place to pick up partners?
Rifle. There is a lively scene there every summer, and (despite the bad reputation) people are very friendly. The layout of the canyon is such that you can easily roll through and find people to climb with. It is one of the easiest places to find partners that I have visited. You can pretty much just go to the Ruckman Cave/Meat Wall parking in the morning on sit on the bumper of your car, and you will have a climbing partner within a half hour.
You can also find Front Range partners easily through this site. However, I have always found that, when on a climbing trip, it is easier and more reliable to just go to a major area and find partners in-person, instead of doing the online thing.
Jon Frisby wrote: 3) Weather? Otherwise I'd just hitch to Shelf
For sport climbing, Independence Pass is at elevation and is often reasonably cool. Many walls face south, though, so the shade game can be tricky. Devil's Head is high up too and can be nice in the summer; some walls get all day shade. Rifle will be nice in the morning and sweaty but climbable in the afternoon. Due to steepness, the afternoon storms aren't a dealbreaker for many of the walls in Rifle. Shade is easily found at any time of day. Clear Creek and other Front Range foothill crags can be very sweaty, but still climbable with morning shade. The sport climbing on the steep west faces of the flatirons is awesome, and has good shady morning conditions. Shelf will be a furnace.
For bouldering, RMNP and Mt. Evans offer the best conditions, although storms can/will be an issue. Going to that elevation straight from sea level would also be pretty rough.
For trad climbing, the alpine stuff in RMNP and at Evans is best. Lumpy is at elevation, but faces due-fricken-south and bakes. Some of the north/west facing stuff in Eldo can be reasonably nice in the morning.