It sounds like you are inside the beltway, possibly in Alexandria? I don't know of much in Alexandria, but Arlington is right next door...
We enjoy going to Long Branch Nature Center on Carlin Springs Road in Arlington. They have an indoor turtle pond (well fenced!), various reptiles in terrariums to look at, and a children's play room that has among other things: a play house full of stuffed animals, puzzles, toy dinosaurs, fishing poles and magnetic fish, crayons and pictures to color, etc. We can be there for hours! Sometimes it is a bit hectic when they are running the childrens' programs (The Snag for Wee Ones is the name of the program).
The Barcroft Center in Arlington runs an indoor play area, I believe it is on Tuesdays and Thursdays in the morning (we went last winter, now we are doing preschool). There is a fee, $3 or so. It is a gymnasium with bikes, balls, mats, and other toys, and you can bring your own toys, too. Check out other community centers near you to see if they have a play area program.
I recommend checking out the libraries in your area. We go to Central Library in Arlington and they have a large children's section with puzzles, a large wooden activity cube, and a shelf of board books for LOs.
I hope these suggestions help!