The Denver Milk Market is right downtown and has lots of food and shopping options. It is fun just to pop in for a coffee or to shop for some local keepsakes.
If you're looking for some outdoor activity, check out Red Rocks.
If you have some time on your hands, take a drive up to Boulder. About 40 minutes from Denver with beautiful views of the flatirons. Once you are there, visit Chautauqua Park for beautiful views of the flatirons and lots of hiking options. You can also visit Pearl Street for tons of restaurants and shopping (and people watching).
Union station is where the train from the airport stops. It also has several restaurants, shops, and bars. There you can find an open air bar, the Terminal Bar. Another good option here is Cooper Lounge for trendy cocktails.
RiNo is a great area to have an uber drop you off and just wander around. There is a local brewery just about every few steps. There are also lots of good restaurants and shops to visit.