Road Trip Through Tennessee and Virginia and Vacation in Washington DC

Sevierville TN near Gatlinburg used to have a deer farm where you can pet and feed the reindeer. It might still be there.
TN also has Graceland.
Richmond has a Children's museum and a science museum with hands on activities and a really cool bug room.
the Air and Space Museum in DC
the National Zoo, a must do with a 4 yo.
King's Dominion is right here and is great!! But since mine are older I don't know about little one's rides.
Busch Gardens is in Williamsburg and is fun, more shows that KD but KD has better rollercoasters, that is of you are 13 and 16.
Williamsburg is a lot of walking. It can also get really crowded. You will get a ton out of it she may get bored, it's a lot of talking to people pretending to be so and so. My kids love it now but they are a preteen and teens.
It is about 2 hours from DC.
Stay south of the city when you come, or west. THere is Manassas, Woodbridge, Stafford, Springfield. Take the Metro as often as you can. Take a stroller. And wear comfortable shoes. Food is crazy expensive on the Mall and McD's is no where to be found. So bring snacks and a day pack with drawsrings, and water.
Parking is hard to find.
It's fun to walk the monuments. YOu can take a picnic and rent one of those paddle boats for the tidal basin.

If you plan on spending July 4 in DC be warned now. Last year there were over a million of us up there. Food was scarce, water was $3 a bottle. Fireworks were fantastic but not worth the hassle.

Nashville has several historical sites if that kind of thing interests you - and most are filled w/folks in period costume to tell you about them. (the Hermitage, etc - not just country music related!)

There is a mule-drawn canal boat ride in the Georgetown area of DC (presume it's there and they fixed more of the canal) - if your 4yo is one of the few children on, you might get lucky and child could be "co-captain" !

Pidgeon Forge/Gatlinburg area in Tennessee, it is just about 20 minutes from Knoxville. The mountains are gorgeous, there are hiking trails in the Smoky Mtn National Park. tons of shopping and things to do. Dollywood is there too. In DC, I agree, there are lots of things to do there and it is pretty much all free. The museums, especially. Plus all the surrounding areas, such as Arlington and Alexandria Virginia are pretty, and Mt Vernon is very nice. I have not been to Colonial Williamsburg in years, and don't really remember much about it (I was pretty young).

I don't know what to do with a 4 year old, while going to DC, but check and see if the Children's Mueseum in DC is open. It's great and the kids can touch everything. I know it was closed for renovations, but I think it should be open by now. There is also the National Zoo, which is 100% better than the Dallas Zoo (in my opinion). There is the air and space museum. If you are willing to travel another 45 minutes to Baltimore, there is Port Discovery, which is a children's museum, the harbor, and the aquarium. Almost all of the museums in DC are free, so google smithsonian, and it will give you links to all of the smithsonian run museums in DC. I don't know if you are sports fans, but I hear Nationals ballpark is amazing. Also, you will be near Great Falls, both Maryland and Virginia. Great hiking (though not too much for a 4 year old) and views of the Potomac. Oh yeah, right outside of Richmond, is Kings Dominion. It's like Six Flags, but better.

To address a few things other said: The Children's Museum in DC is closed and has been for several years. It's supposed to reopen in a new location in Maryland, way too far from downtown, but I have heard nothing at all about that new facility and doubt it's even under way.

Wiliamsburg is more than two hours from DC. It's easily three hours. I love it and my girl loved it at five, but at four it may be too exhausting -- lots of walking, very crowded in summer, and that area of Va. is extremely hot and very, very humid in the summer (mid-June to mid-Sept.) Check their website at www.colonialwilliamsburg.com (may be a dot-org) to see if they have enough young-kid-friendly stuff to be worth it but I would wait if you want your child to have fun there.

Places for 4-year-olds in DC itself: National Zoo, yes. And go to www.si.edu for the whole Smithsonian world including: Museum of Natural History (dinosaurs galore, animals if he/she doesn't mind seeing them "stuffed," a kids hands-on room but its hours are limited, check before going); American History Museum (be sure to take kids to the SparkLab and the Invention at Play exhibits, they're hands-on). There is an antique carousel on the National Mall (the green space between the Washington Monument and the Capitol). Check washingtonpost.com for a lot of listings and search under kids activities. There are also kids activities at the Smithsonian but check the web site for details. DC area has several theatres that do shows for kids -- excellent.

Richmond has a children's museum and a science museum that's good for kids too. Look them up online.

If you are planning to come in summer, like I said, the DC area and Va. are very humid and nastily hot. I'm not discouraging you! Just be ready to get inside frequently and carry plenty of water!

I think Williamsburg is fun. We went to a dinner theatre one night with the kids (they were a little older, but the kids might have fun anyway). You can also check out Bush Gardens for a day.

In DC there are tons of things - don't bother with the aquarium there (go to Baltimore if kiddo likes fish) but all the Smithsonian museums, the Spy Museum, the Newseum, there might still be duck tours (amphibious vehicles that go in the water), the ZOO.