We used to live right across the street from the King Street Metro--either of the hotels right there would be perfect. If we moved away and were coming back for a visit, that's where I'd choose to stay. It's nice to go into DC during the day and walk down King Street to a restaurant or to the waterfront in the evening. It's very safe. Lots of cute shops up and down King Street as well. There used to be evening riverboat tours to Mount Vernon or the monuments down by the waterfront, not sure if that's still available, but we enjoyed that.
You might also want to check on Amtrak prices--the Alexandria stop is right there by the hotels, very easy walking distance. We love taking the train to and from New York.
Everyone has hit all the great spots already--I would definitely just do museum food courts during the day and try for something more interesting in the evenings. The food court in the modern art museum, the East Gallery, is pretty cool--a waterfall from above flows across a big window. But the food there is nothing special. It's on the very corner of the mall, a bit of a hike for a 7 year old. If you're trying to hit monuments on the other end, you can also stop at the Old Post Office--there's a large food court there and the Federal Triangle metro is right there.
When you get on the metro, you'll want to wait for the Blue Line to get to the Smithsonian stop (you'll see Blue or Yellow on the front of the bus, like at Disney). When you buy your farecard, there's a chart that shows your starting point and your ending point and how much the fare is--pay attention to the times, fares are different during rush hour. You can buy daily passes for unlimited travel, but that may not work for you because there are restricted times on those during the week. If you're just going King Street to Smithsonian and back, I think an individual card might work better. You asked if it's a subway--part of it goes underground and part is above ground. Federal Triangle also has a blue line so you're good to go if you go to the Post Office for lunch and decide to head home. The Pentagon City Mall is also right on the blue line so that's an option, too. They have a food court and lots of different restaurants. The stop is right under the mall, just get off and follow the signs up.
Don't hesitate to ask for help--I rode the metro for years and helped tourists all the time, no one minds. Just make sure you stand on the right side of the escalators (left side is for walking/running) and no food or drink, they will bust you with a fine. Don't panic if you get off and don't have enough money on your farecard to "get out" (this can happen if your timing is off for rush hour/non-rush hour). You can add money to your card on one of the machines. I remember a thread about the people in DC being unfriendly, but generally people are in their own little worlds, just trying to get to and from work, and are happy to help if you have a question.
Hope you have a good time!
