If you only have a few hours I would recommend the following:
Check your luggage into the storage room ASAP and jump on the Metro RED LINE to "Metro Center' station (2 stops from Union Station). Take the 11th Street exit stairs and head 2 blocks south for the FORD's THEATER NATIONAL HISTORIC SITE where President Lincoln was shot, and across the street is the house he died in. This will take about 90 minutes total of your time and still get you back in time to eat and make your train.
If you end up with 5-6 HOURS sightseeing time, immediately check your luggage into storage and take a taxi to ONE of the Smithsonian Museums, the Air and Space Museum being closest, the American History or Natural History museums being the furthest on the National Mall,.
From the National Mall it is about a 15-20 walk past the FBI Building up to the Fords Theater, then you can take the RED LINE Metro back to Union Station.
Allow 2 hours per museum on the Mall if you attempt to see more than one, and plenty of time for going back and forth in the DC traffic if you are using taxi's!
It takes about 25-30 miutes to walk from the A&S museum back to Union Station, most of it up a slowly inclining set of streets. If you are in good health it is a nice walk past the Reflecting Pool and the Capital Building.