re: Washington DC trip with kids (10 & 12yo)

Just went to DC for the first time a few months ago. Stayed at the Willard in a suite, but I'm a baller. The best mode of transportation is the Big Bus. It's a double decke/open top tour bus, and it will get you everywhere. You buy a pass for a few days, and you can hop on and off at all of the attractions throughout the day. There is a bus stopping at all the stops like every 10 or 15 minutes. There are several different color-coded routes, and each route hits a certain group of attractions. So lets say you want to see two things on opposite ends of the city. You'll take the red bus to see one attraction, and from there hop on the yellow bus that runs a completely different loop. And they also do a night tour that hits the major attractions.
Make sure you select a hotel based on location first and foremost. Google a map that shows the city layout and all the hotel locations, and pick anything close to the National Mall. You'll be surprised how many things are within walking distance, though expect to do a lot of walking. We went thinking we'd use the metro or cabs, but the Big Bus was all we needed. It took us everywhere we wanted to go in an inexpensive and very convenient manner.