Yeah, if you stay in Banff, you can drive to Lake Louise in about 30-45 mins depending on conditions. Mount Norquay and Sunshine are minutes away from Banff and Nakiska is about 30-45 mins away. If you want to stretch it, you can drive a couple of hours west of Banff and do Kicking Horse. Next on the road is Revelstoke, about another hours west of Kicking Horse. Banff is your typical touristy ski town with all the good and bad that entails, be warned! :-)
Lake Louise is the best skier's mountain...Sunshine is a neat above-treeline kind of experience but spread out and broken up. Norquay is literally across the highway from Banff and is still a challenging hill. Nakiska was built up for the Olympics in 1988 and has been improved recently with a high-speed summit lift that makes it a bit more complete.