Admission to the monument is free, but you do need a ticket since they can only let so many people in at one time. It's very tiny at the top. As a note, if you order your tickets online, there is a $1.50 service charge.
At the top of the tower, there are two windows on each of the four sides. While it is a little difficult to fit into the space near the window (unless you are a child), it is possible. You can see about 30 miles in each direction. That means you'll be able to see both Maryland and Virginia. I'm not particularly fond of heights but I did find the view impressive. (I stood in the back by the elevators instead of going right up to the window.)
The longest part of the museum is the elevator ride up and down. If you have a half hour or so to spare during your trip, you should check out the monument. It's just plain neat.