Chesapeake Beach Water Park

Sandy Point Park

Baltimore harbor

I'd take him/her up to a farm and do some berry picking. My kids love to go and if your child still naps they can sleep on the way home. We like larriland up in MD but there are lots of others. Strawberries are starting this weekend (probably a bit scattered at first)

When I had a 2-year-old, Dutch Wonderland and even Sesame were not too far. Leave early, and the child might sleep on the way up and the way back.

Ive done Dutch Wonderland for the last 2 years with my now almost 4 yo. So the first time we went she had just turned 2 ( June bday) Its totally doable. I think it would be boring to go by yourself with a 2yo though unless you have another adult going.
We live in Silver Spring and its an hour and 45 mins from us.

Philadelphia. Take them to the Please Touch museum.

The Aviation Museum in College Park is small (much less crazed than Air & Space) and has great hands on things for kids to explore.

There's also the National Capital Trolley Museum: http://www.dctrolley.org
It's smaller, but includes a nice train ride.

My 2YO stayed in the stroller at Luray. He liked it, but we were there for the older kid. It's a long drive for a daytrip.

Port Discovery is worth the drive to Balto.

Frying Pan is perfect for a 2YO. I am so over Udvar... never again.

If you haven't already done the playroom at the National Building Museum, give that a try.

Luray Cavern

We're doing Sesame this year in one day, but with our 4 y/o who doesn't nap much. I don't think we'd do it with a napping child. Stay within an hour of your home.

Frying Pan Park in Fairfax County--near. Dulles. Then go to Udvar-Hazy. Great combination: baby farm animals and airplanes. Total cost: parking at Udvar Hazy. The park and the museum are only ten minutes apart at most.

We did baltimores port discovery yesterday with our 2.5 year old. Had a great time in the water area, sand area, "catching" butterflies, cooking in the play kitchen, playing in the diner and grocery store areas.

I guess you're trying to get out of DC, but really there are so many museums, monuments, etc in DC that going elsewhere is kind of superfluous.
When they were young, going to the park that is at the end of National's runway was good for an hour or so of fun. Planes come in so low!

Frederick- There is a train near there, the keys baseball game, and downtown parks.

Harpers Ferry

Are you specifically looking at amusement parks?

We did Hershey last summer in one day with my then-2 yo.

If you want to broaden your scope:
B&O museum in B'more
Aquarium in B'more
Zoo in B'more (has been renovated since I went there as a kid and is really nice)
Port Discovery in B'more
North Beach in Calvert County

Wanted to go to Dutch or Sesame but I realize its too far for a one day trip with a 2 yo. Any ideas for something a little more local?