I've lived in Estes Park half-time for the last few years and am very familiar with the east side of RMNP.
You'll want to figure out about East Side (Estes Park) vs West Side (Grand Lake), which are connected via Trail Ridge Road. Both will still be busy that time of year, between festivals, the elk rut, and the aspen. There's a chance, especially late into October, that Trail Ridge Road could close and that will affect your ability to get to and from Grand Lake.
There is a really nice campsite near Mills Lake and also some great campsites in Wild Basin. If you have trouble with some of those, there are some good ones on the North side (Cow Creek area). As alluring as Longs Peak can be, I wouldn't recommend camping at the Boulder Fields as it gets really windy.
You can find some great trails, including all the stats, at
http://www.rockymountainhikingtrails.com. A few of my favorite trails are Mills Lake and beyond, Chasm Lake, Flattop Mountain and beyond, Gem Lake, Twin Sisters, Lion Lakes, and Thunder Lake.
I'd recommend using the Gaia GPS app where you can download offline maps and possibly a satellite tracker like an inReach as most of the park is out of cell coverage. As mentioned, be prepared for snow at higher elevations. You may need microspikes for traction. You can always pick up any last-minute gear at the Estes Park Mountain Shop or an REI.