What to Do
If you plan on exploring the monuments and memorials, keep in mind that the walking distance between each one is no joke, so definitely bring that stroller! The Washington Monument is always impressive, and if you want to ascend to the top of the obelisk, pick up timed tickets in advance so you won't have to wait on line the day of your visit. The kids also loved the grand fountains of the World War II Memorial.
A fun way to get a panoramic view of the area without all the walking is by renting a paddle boat and cruising around the Tidal Basin. These can also be reserved in advance on the weekdays.
One of the best things about DC is that the 19 Smithsonian museums and galleries are all free. This includes the impressive National Air and Space Museum, which is seriously great for all ages. View a land rover up close. Touch a real piece of the moon. See the actual Wright Brothers' airplane. Watch an IMAX or planetarium movie. You could spend an entire morning or afternoon exploring this fun and interactive museum.
Where to Eat
For a great meal in an atmospheric setting any time of day, our favorite restaurant in DC is Ted's Bulletin (there are two locations), an old-timey diner that will make you feel like you've stepped into the 1940s; even the waitstaff is dressed accordingly. In addition to the fun décor, Ted's serves huge portions of seriously good food. End your meal with a Ted's Tart, their version of Pop-Tarts that's freshly made on the premises and comes in a variety of flavors.
Another good place to eat with the kids is Open City, a diner located near the National Zoo that's perfect for a sit-down lunch or to-go beverages.
What's Nearby
A few subway stops north of all the monuments and museums is the National Zoo, another free attraction that's well worth a visit, if only for the panda exhibit. (Did you know that only four zoos in the country house pandas?) In addition to the exhibits, my kids enjoyed taking a spin on the solar-powered carousel that features more than 50 different zoo animals.