1. Daydream is right. The metro is pretty easy, the only thing you have to do, is look at the little map and find the direction you’re going, and then what the end point of that direction are. The lines aren’t announces “Orange East” or “Blue East” for example, they’re “Orange/Bue to Largo/New Carrolton.” It’s easy figure out, but that’s the only thing I could see being to figure out.
Also, I didn’t look at the dates, but generally the metro usually sucks on the weekend. It works, but the weekend is when they do work on it, which delays the trains. Be prepared to wait in the ballpark of 10-15 minutes for a train, and again for a connection if you’re making one. That said, its generally not worth it if you’re only going one stop. The downtown stations are all REALLY close together, and downtown is very walkable. If you’re going pretty far out, it’s a must.
2. Things to do that aren’t federal: I’ve found that walking around the monuments is a LOT more fun at night when they are all lit up. I’m not sure if this would change if the government closes, but its a thought. The Newseum is definitely about $20.00/person for adults but again, and while we went with free tickets, FI & I agreed that it would have been worth paying the fee. Other privately owned museums that are said to be worth the price (but we haven’t made it to yet) are the National Geographic Museum and the Spy Museum. Sorry I can’t offer more info on those though.
If you’re into dancing & parties there are a lot of little bars & clubs along U Street and also 18th Street in Adams Morgan. If you make the trek to Adam’s Morgan and are feeling adventurous, try some Ethiopian food! DC has one of the largest Ethiopian communities in the US and there are a few resturants in this neighboorhood that are excellent.
I’m less of a fan of Eastern Market than a lot of others. If you have a farmers market in your hometown, its probably better than EM. If you like little streetfair type yard art, etc. though, it might be a lot of fun.
Overall, I’d say “Don’t be afraid to leave the mall.” Obviously, any vacation kind of depends on your budget, but there are a lot of fun little places to explore. Honestly, one of my favorite things to do is to take a walk or run through the Capitol Hill neighborhood. Its beautiful this time of year, its close to me (I live in Hill East) and its free!
Have a great time!