If you're coming from SD, your first logical choice might be Estes Park. Just take your car and stay at one of the motels in town. Then you can visit the east side of RMNP, plus drive along the peak-to-peak highway to Idaho Springs. I wouldn't bother going all the way to Grand Lake as the aspen aren't as thick there. Leaves in this area generally peak around the third week of September. As noted, it get's very busy in the park that time of year, but if you travel on weekdays, things aren't quite so bad.
As mentioned, the area around Buena Vista and Salida have good aspen displays. The road up to and esp. above St. Elmo has whole hillsides with nothing but aspen. Being further south, this area tends to change closer to the end of September. The nice thing about this area is you have flexibility. Head up to Leadville if the leaves around Salida aren't changing yet, or head south to Salida if the leaves around Leadville have dropped. The road north from Leadville to Minturn (US 24) also has good displays. From Leadville, you can also head over Independence Pass to Aspen (might be some aspens around there!). From Aspen, head up to Maroon Bells somewhere around the 3rd week of September for fantastic yellows against the red of the mountains below azure skies. If you hit the leaves and weather there at the right time, those pictures will be the highlight of your trip. We enjoy Salida as the downtown has undergone a nice rejuvenation with some quality restaurants and interesting art shops, antique shops, etc. without being too upscale or pretentious.
Your car will give you a lot more flexibility. Plus, some CG's in CO close right after Labor Day.
But IDman noted, there are some places where a few aspen are beginning to change. We heard elk bugling above Unaweep Canyon at the north end of the Uncompahgres two weeks ago, and others I've talked to have heard them bugling in the hills south of Glenwood more than a week ago, so it may be an early winter.