Well, there are lots of opportunities to do the typical touristy things like wildlife watching, hiking, skiing, snowshoeing, white water rafting, mountain biking, etc. I will just warn you that Banff is a beautiful place but rather expensive to do any shopping or staying in general....a tourist trap if there ever was one. You can check this site out
http://www.banfflakelouise.com/Things-To-Do/ for some ideas. I do recommend heading to the Columbia Ice Field to have a mosey about on the glacier...they even have a special vehicle that will drive right up and onto it. You may also want to consider heading south a bit to
Radium Hotsprings for a splash in those lovely pools. The whole area from Jasper to Banff to Radium and right down to the U.S. border is chock full of outdoorsy opportunities with vast stretches of wilderness.
As for places to stay, all depends on your wallet. You can stay at some palatial hotels or roughing it with some camping in countless provincial parks. B&B maybe a good option and/or a stay at log cabin. It is a huge area we are talking about but with a good travel agent or just some intensive Googling you should be able to sniff out some decent deals and amazing places to stay, summer or winter.
