What else is there to do besides looking at the memorial & (Obviously enjoying it?)

There are a number of monuments/memorials in the area. Lincoln, Vietnam, Korea, FDR, Jefferson.

There is the Jackson, Lincoln memorials. Capitol national mall, etc. DC feels like a field trip to me.

They have plenty of museums, free of charge, like the Space & Air, Smithsonian, Natural History, the White House, US Capitol, Library of Congress and much more. You can Uber to all these place or just walk. Make sure that you stay close to the National Mall (name of the area with all these museums and monuments).