What kind of advice are you looking for? Do you know where you are staying? Will you have a car? It will be cold here. If you aren't driving the metro is pretty easy and much cleaner and safer than NYC.
If you want something off the beaten path, the National Museum of Health and Medicine is fascinating:
www.medicalmuseum.mil
Depending on when you get here, you might still be able to see the Mormon Temple Lights -- they have a light display outside, and an exhibit inside (one year it was trees and dolls from around the world) and a concert each night:
http://dctemplelights.lds.org/ It's about 15-20 minutes outside the city, so you would need a car.
The National Zoo also has a light display:
http://nationalzoo.si.edu/activitiesandevents/celebrations/zoolights/
Rock Creek Park is a local favorite -- check out the schedule to see what's going on while you are here. They have a planetarium.
http://www.nps.gov/rocr/planyourvisit/things2do.htm
Again off the beaten path, not a lot of folks know if you plan in advance you can tour the Naval Observatory. You can see one of the master clocks (how the USG officially keeps time) and one or two of their large telescopes.
http://www.usno.navy.mil/USNO/tours-events/tour-information
See a show at the Kennedy Center -- they have kid friendly performances too:
http://www.kennedy-center.org/index.cfm
Where to eat.. Open City Diner is fab -- and you get animal crackers with your coffee/cocoa. Fantastic brunch - gets crowded on the weekend, but the wait usually isn't bad:
http://www.opencitydc.com/
Old Ebbit Grill is classic DC:
http://ebbitt.com/ They will probably still have these amazing giant nutcrackers standing guard out front.
Ben's Chili Bowl is a landmark:
http://benschilibowl.com/
What else would you like to know?