Taggert Lake is a good one. If the weather is a bit cool/cold/sleety/snowy, you might be better off with a valley hike. Along the lines of Taggert Lake (and these are all in the park):
Hermitage Point. Leave from Colter Bay (a half hour drive from park entrance). Flat hike to Jackson Lake with excellent views of Mt. Moran framed by golden cottonwoods and willows. A good half day hike.
String Lake/ Leigh Lake/ Jenny Lake. Depending on time, distance, and combinations, this could be a nice half day or a pretty full day hike. Many options. One would be to start from String Lake parking, head north to Leigh Lake along shore of STring Lake (beautiful), back to sign pointing to Paintbrush Canyon, head west (right) then take the left trail to Jenny Lake. You could loop back to parking at this point or continue along west side of Jenny Lake to Cascade Canyon. From here you can go west to Hidden Falls and Inspiration Point for great views of lake and valley. To make it a full day, you could continue up Cascade for a few miles looking for moose and perhaps a black bear. Return along Jenny Lake to String Lake parking.
Hikes with more UP to them would include the aforementioned Cascade Canyon all the way to Lake Solitude. In summer, this is filled with people, but I'm sure that it will be very quiet in October. Start from Jenny Lake parking, hike around lake (in summer a ferry boat service is operating but I suspect they've closed for the season) then continue about 8.5 miles up canyon. Lake Solitude is very pretty with some excellent views of the back of Mt. Owen, Teewinot, and The Grand.
Another killer UP hike is Ampitheater Lake. Start from the Lupine Meadow parking. Starts out nice, then goes up with lots-o-switchbacks. The rewards are fantastic views of the valley and Surprise and Ampitheater Lakes. This would be a full day hike as well.