Take a little time out of your day to walk a loop at the park. It's a great place to see what Flagstaff is really about. You'll often see deer hanging out while people take their dogs for a walk or a run. You'll get great views of the San Francisco Peaks, Mount Elden, and it's also a great place to get some mellow exercise while in nature.
Get coffee at Macy's, Rendezvous, or Late for the Train, enjoy a beer at one of the many microbreweries, eat some fantastic food, listen to music (either on a corner or in an establishment), or join in whatever festivities are happening in Heritage Square.
The Pioneer Museum is easy to spot along Highway 180 due to the well-preserved steam engine and boxcars dating from 1929 out in front of the main building. The museum is housed in a former hospital dating from 1908 and displays artifacts and other items from the early days of Flagstaff. The focus is on the development of Flagstaff from 1880 to 1960 and features information and exhibits on the logging and ranching history of the area, with rooms dedicated to each decade. Outside the main museum building are expansive grounds showcasing Ben Doney's one room cabin, a 1915 Model T Ford, and a Fire Engine that saved nearby Riordan Mansion.