Gravelly Point Park is just outside the city in Arlington, Virginia. Great place for toddlers to enjoy ambling around and watching the planes take off and land at Ronald Reagan National Airport.
If your kids love airplanes, this is the place to go. Bring your picnic blanket, food, frisbees and lawn chairs. There are a few picnic tables, but in case they are full, you will want to spread out on the large grassy area.
If the wind is coming out of the south, the planes will come directly -- and I mean DIRECTLY -- over you. You will feel like they are going to land on top of you! They rumble and block out the sun, giving you a most unique sensation. There are also some terrific photo opportunities here. If the wind blows from the north, the planes land on a different runway, but they are still up close and fun to watch.
If noise is a problem for your kids, bring earplugs. There are some portable toilets here, but not much else (no stores or anything). You are right next to the water and a nice bike/walk/jogging trail. There is a parking lot, but it does tend to get full on beautiful days and weekends. You can circle for a while and hope to catch someone who is leaving.
Have fun!