Your plan sounds pretty good. Just be prepared to do some walking as things are pretty spread out.

The Americana is indeed in Crystal City (which is really just a part of Arlington) and it's just a couple of blocks from the Metro (subway) station. Note that Crystal City is a bit confusing at first because all the buildings look alike, but if you can find the big Marriott Hotel (there's also a small Marriott a block away - very confusing) you'll find the Metro station because it's right behind it.

Do not drive into DC; traffic can be bad, the roads are very confusing, and parking is difficult to find. The Metro Blue line will take you to Arlington Cemetery (Arlington Cemetery stop) and the monuments (Foggy Bottom stop). For the museums you can again take the Blue line (Smithsonian stop) or take the Yellow line (shorter ride, L'Enfant Plaza stop) and walk a couple of blocks.

You might try the monuments at night your first night as you will be getting in late in the afternoon. You do not need to take a tour, just hop on the Metro, as the National Mall area is quite safe after dark.

Driving to Alexandria and Mt. Vernon is no problem. Alexandria is also your closest place for a selection of good restauraunts (though there are a few in Crystal City).

Make sure to hit Gettysburg on a weekday, and hopefully not in the summer, as it gets very crowded. After seeing the cyclorama, you can buy a CD self-guided tour and then just drive around the battleground at your own pace.