Here's some good information on the subject... and many more subjects for the park on the park's web site. Explore this site thoroughly for lots of good information.
Ernie, we were there in September, and it was wonderful -- fall color and somewhat fewer folks. But don't make the mistake we almost made -- I decided not to go to the East side of the park because it was too crowded. Fortunately, DW decided I was wrong (nicely, of course).
She was right. Even if it is crowded, spend some time on the east side of the park, as well as the west side. There is a good reason that the whole park is crowded -- it is terrific.
Probably right after school stops, but check with the park to see if Trail Ridge Road is open before you leave. They have had a lot of snow in the Rockies this year and access to that road may be late.