If you will be exploring downtown Denver, the 16th Street Pedestrian mall has a free hop on/hop off bus that can get you close to eateries, closer to the Pepsi Center, the Denver Center for Performing Arts theaters, within walking distance of the art museum+.
Downtown also has PediCabs - speak with a driver to set up a fee for an area tour.
In Estes Park you can drive a nice loop to see the fall colors, stop to take a walk along short trails and also arrange for horseback riding to catch a glimpse of the fall colors. Late September is the time for elk bugling - a cool thing to hear late in the afternoons inside the park.

First, you will not "see" Colorado in 3 days. Pick one area, perhaps RMNP, Grand Lake, Winter Park & back to Denver or just RMNP. Or Summit County and a drive to Glenwood Springs. Do not try to do too much or go too far.

That's a great time to visit Colorado, the aspens will be around peak golden color and the weather can be spectacular. I'd recommend a route with maximum views is from Denver to Boulder, lunch there, then up Boulder Canyon to Nederland, then north to Estes Park along the Peak-to-Peak Highway. Then you can spend the rest of the time in Rocky Mountain National Park. Estes would be the best place to stay, with daily drives into the park, including over Trail Ridge Road. It's elk rut season, and that is something to see and hear! There are great little lodges and cabins along Fall River Road, but reserve quickly since it's prime time. Coming back to Denver, go east on Hwy 34 through the Big Thompson Canyon to Loveland. You can certainly see some great mountain scenery on this route! It's just a small area of the state, but one of the best!

I would do as Tekwriter suggests up to the Park on Tuesday afternoon. Stay in Estes that night.
Then I'd drive on through the Park Wednesday over Trail Ridge Road to the other side of the Park.
Take Route 9 (I believe) through Kremmeling down to I70 at Silverthorne, and enjoy a pleasant drive through the Rockies on the Interstate.
YOu could drive to Glenwood Springs for that night pretty easily. Do see the Glenwood Canyon exhibit about building the road there.
Thursday drive back to Denver--maybe the real Coloradoans can direct you how to do that through Leadville, etc.

You could also start the other way - say going first up to the "Suimmit" (with towns/ski areas such as Frisco, Breckinridge, Keystone, A-Basin, 20 minutes from Vail, etc) - and that is a couple of hours/plus? - pretty much all freeway - from the Airport.

After exploring that area you could then take the "back way" to Estes Park/RNMP - and then your last afternoon/night - stay in Boulder - a very neat University town - which is only 45 miles from the Denver airport, but check with the locals as to what rush hour there may be going that way in the morning. I wouldn't think too much.

Here for example is a map of driving north from Frisco to Estes Park - and while this shows the most direct route (which we took) - you could also take a combo of the different roads - combing the longest route - starting on 9 and up and over to 40 - or going up 40 to 34 - and over - eventually to Estes Park. But any of these routes would allow you to really see a whole lot of Rocky Mountain National park - assuming there wasn't an early snow storm, etc.

http://www.distancebetweencities.net/frisco_co_and_estes-park_co/route

And for RMNP itself. http://www.nps.gov/romo/planyourvisit/maps.htm

As BetsyG said (unfortunately or fortunately!) you will not be able to see all in 3 days. I suggest you to check what other travellers have done and mapped on http://www.goprotravelling.com and afterwards map yours and contribute too.

I will say for travelmapper (advertising?) that we have actually DONE the route I suggested, in that time frame, but never put it on that site.
AND finally on a Friday at DIA do not cut your time short to get from returning a car to the gate, through security. We have been there often when the maze was full.
If you do put Boulder in your itinerary anywhere, try to do the Celestial Seasonings tour. It is fun and informative.

ditto-DEN can really get backed up at security for some reason.
Allow the full 2 hours as they suggest and you should be ok.

It was Snowing this morning at the I-70 tunnel.
Just a reminder that the weather this time of year swings; downtown Denver started at 50 degrees, the Estes Park area was 34; daytime temps = perfect.

Just to be clear, the full 2 hours INSIDE DIA, not at the car rental office.

Thanks for the helpful replies! Yes, I realize we can't see all of Colorado in the brief time we have. I was just wanting to get some suggested routes that would let us see some of the highlights of the state in the time we have. I still can't decide which way to go, though. I really would like to go to Aspen and see the Maroon Bells. Would it be possible to do that and RMNP/ Estes?
I'm excited to hear about the snow! In the long-range weather forecast, I saw that there's a chance of snow while we're there.
Gretchen, thanks for the head's up about the airport. We'll keep that in mind for our return flight. Thankfully, we don't leave until noon on Sat.

I'm an occasional business visitor to Denver. As others have mentioned, RMNP is quite close and should be spectacular.

Also, Red Rocks amphitheater is really beautiful and good for some short hikes. It's an easy drive, and something I've gone to after I finished up work for the day. No aspens, but rock formations like Sedona and lots of wildlife. There is a natural amphitheater there, and concerts are held there in the summer.

It snowed some here yesterday in the mountains to the west of Denver. You may well get some snow.

Yes, with my suggestion of driving through the park and on to Glenwood and Aspen. I can't quite remember how long the drive through the park and down to Silverthorne is--maybe 4 hours total? Then Aspen is about 3 hours from Silverthorne. The drive through the park is at a leisurely pace, mind you. Aspen is 4 hours from DIA going directly, for an idea.

Today I hiked up a 13'er in the Indian Peaks, just south of RMNP. Any snow that fell there is melted except for occasional pockets under north facing rocks. Not visible at all from a distance. There was a strange light haze in the air (northwest fires?) but we all agreed it made everything look ethereal.

However the aspen above ~9,000 are now changing nicely, better than reports led us to expect. There were some nice pockets of red colored aspen. And the tundra colors were truly superb.

You could do Estes and Aspen in 4 days: Denver - Estes - Trail Ridge - Grand Lake - Vail - Glenwood - - Aspen as suggested above. Driving time per Google of that route is 12-13 hours. That's a lot of driving for me but since you want a driving trip I'd say go for it. But make a final decision when you arrive based on weather situation. Lodging should not be an issue.

If it snows hopefully it stays up high, above timberline, or else it will quickly end the aspen color. I got to see that twice in the Bells: aspen changing and snow high on the peaks. It was worth driving all day to see!

Good luck.

Nelson's answer above for the time of driving surprised me, since we have done something similar to it and was sure it wasn't that amount of time.
Googling finds the driving time to be almost exactly what I suggested, via Trail Ridge Road to Silverthorne. And even better, drive through the park on Trail Ridge road and down to Silverthorne--about 4 hours. Then take the "back" road to Aspen from Breckenridge (Route 24) through Leadville to Aspen--another approximately 3 hours, and fun scenery.
Coming back to DIA you can take the road from Aspen to I70 and be about 4 hours drive for your last night.

Gretchen, you are correct. I forgot to add "back to Denver from Aspen" in my description, but I was counting that in the 12 hours. So I think we are close in the times.

Thanks for the correction.

I will go against the flow and recommend you skip RMNP and head directly to Aspen, if that is the place you have in mind. There is so much to do there, and the scenery is majestic, so I don't think you would be shortchanging yourself not to see the park this time. Simply because it is a lot of driving to do both. And we love Aspen.

Please note that this past weekend the fall colors were at their peak in the Aspen area and may be finished by time you get there. It's possible that Trail Ridge road may be closed the last weekend in September, although the forecast looks good for now. If open I would definitely take that route as it's spectacular. Otherwise missing RMNP and driving to Aspen may be the better option. Regardless of which you choose, the scenery is absolutely beautiful IMO.

The Goggle time is very optimist since it never gets stuck behind a slow moving truck on a curvy road or makes any provision for stopping and just looking. Given your limited time, I would skip RMNP since there is nothing there that you will not see somewhere else. The drive through the Glenwood Canyon is awesome and you need to hit a couple of the pull outs. Or better yet, rent bikes and ride the length of the canyon from Glenwood Springs. The drive into Aspen via Independence Pass (Leadville) is as good as it gets. Hike or bike the Mineral Belt trail in Leadville for a unique exposure to the early mining days of Colorado. Try to believe that people once lived there. The drive from Aspen to Denver via I-70 on a good day is 4.5 hours and much worse on a Sunday afternoon.

Last weekend, the colors were just beginning in Winter Park. I wouldn't let the leaf change dictate your trip.

I wouldn't disagree with anything fmpden and PeaceOut are saying. The scenery through the entire trip to Aspen and back, doing the two different routes is just stunning and full of things to see and do.
ENJOY.