Why the town is called Mammoth Lakes. There are many beautiful lakes in town with the easiest to get to being the ones in the Lakes Basin (Twin, Mary, Mamie, George, and Horseshoe). Hang out by the lake, fish, or go on any level of hike near them.
A national monument past Main Lodge in town. Columns of volcanic rock coming up from the ground. It's a relatively short hike that is super interesting.
Mountain biking is super popular in town. You can either bike at the bike park or there are other trails that can be ridden around town. You can rent bikes either in town or at the Mountain.
There are multiple activities that can be done on the Mountain at Mammoth. Some options are the bike park, the adventure center (ropes course, sledding, mountain coaster etc), and a scenic gondola ride.