I live in Colorado, and have lots of friends and relatives from the east coast that come and visit. You never really know what altitude is going to do to you, until you are there.
At 5,000 ft. elevation, the elevation where I live, visitors almost always notice that it takes a little longer to catch their breath than usual. Most people don't get any MORE out-of-breath than usual, but it takes a little longer to stop panting after even a small exertion (like 1-2 flights of stairs). People that are sensitive to elevation can get headaches, but that usually goes away in a 2-3 days.
We always try to make sure that visitors stay at our house for 2-3 days before we head up above 8,000 feet or so. Some people say wait only 24 hours, but we've found that it puts a real damper on their fun if we take them up there that fast. Most of visitors get altitude headaches in the 8,500+ elevation range if you stay up there overnight no matter what. Waiting 2-3 days can make a big difference, though. It can mean the difference between having a little headache that you can ignore while having fun, and having a pretty bad and droning headache, accompanied by feeling bad all-over, and maybe being semi-nauseous.
The roads are not as steep as they are along the west coast, or in the Appalachian Mountains back east, so you probably don't have to worry about any 13% or greater slopes to climb on the bicycle. If you feel the elevation, climbing hills WILL take a little more lung and heart effort than usual, and WILL definitely make you more worn out by the end of the day. If you take it a little bit easier on the climbs, and make sure that you sleep more than you stay up drinking beer and chatting, it should be a damn fun trip.
Oh, and if you are only here for 2-3 days, I would suggest that you stick to riding in the foothills, and only drive and walk around at altitude. The roads over the foothills should be plenty steep-enough for you, and the scenery is usually just as nice as riding way up high (more western canyon-gulch, usually with great views of the Rocky Mountains across valleys and reservoirs and such).
Have fun!