We went on a little get-away last year to Banff in early November, and the hiking was fine (on valley bottom trails) - we walked from town to the hoodoos one day. There was only just a little "skiff" of snow, mostly bare ground and no spikes or cleats needed. It was chilly though (below freezing) and windy; you definitely need warm clothing, mitts/gloves and a warm hat. We also spent a morning at the Whyte Museum, and part of a day just wandering around town, shopping and browsing, went for coffee etc.
There are plenty of other walks to do, and no visit to Banff National Park would be complete without a visit to Lake Louise (but since it's at a higher elevation, expect more wintery conditions there - and note that many of the famous hiking trails have avalanche danger at that time of year, so hiking them is not as simple as adapting one's footwear or outerwear). Johnston Canyon is also worth a visit, even at that time of year; drive the Bow Valley Parkway and watch for wildlife (we saw lots, including a huge bull elk bedded down right beside the road right across from the Johnston Canyon parking lot.) You could visit the gondola, the hot springs ... I don't think you'd have any trouble filling several days. There is also the Banff Mountain Film and Book Festival, which is on until November 4th: http://www.banffcentre.ca/mountainfestival/ (note that weekends, which is when most of the events are on, tend to be busier at that time of year, although weekdays are very quiet).
If you plan on driving part of the Icefields Parkway as a day trip from Banff (recommended), be sure that your rental car is equipped with winter tires (not all season radials) - it is a high elevation road. If you want to drive into BC at all, winter tires are required by law, after October 30th.