Tunnel Mountain is a classic peak that's accessible all year round. Locals bag it after work or for exercise, and some have even summited Banff's smallest mountain hundreds of times! The hiking trail to the summit is just outside the town center and is easily navigable. The trail is well-graded and has a series of switchbacks to the top with several viewpoints, including one with a sublime view of Mt Rundle. It's a great photo point.
Despite being Banff's smallest mountain, it has some great views of the Bow Valley thanks to its position in the center of the valley. It's a great option for a winter hike too, as the trail is often well packed and there is no risk of avalanche.