May 24th 2013, 13:39:55
I'll give you a quick primer and others could probably add more.
I think the Washington Court hotel has had some deals running with $125 a night rooms, so probably $150 after taxes. That's probably about the cheapest you will find in a decent area of the city. It's walkable to the Capitol (maybe 4 or 5 blocks) and from there you can walk down the Mall to all of the museums, monuments, etc. Otherwise, most of the hotels downtown run about $275-400 a night (JW, Hyatt properties, etc).
Most of the museums and monuments are located off of the Orange and Blue Lines on the Metro. So you can look at a number of hotels in VA without having to worry about transferring lines (it's not hard, but just making it a step easier).
In VA, I would suggest Crystal City. It's sort of immediately adjacent to National Airport and Metro-accessible. And if you're really adventurous, there is a way to walk into the city along the river (about 2.5 miles or so from there). Old Town Alexandria is very nice, but the hotels right there are fairly pricey and at their point you may as well have stayed in DC. I think there is a modestly priced hotel in Springfield near the Blue Line's end and there are a handful of hotels near the Huntington Metro Station (Yellow Line in VA), but they're about a mile downhill from the station. The rooms I've seen advertisements for there run from $69-125ish a night, it's not an unsafe area, just old places.
If you go the Montgomery County Route (Red Line) then your best bet is probably Bethesda. I don't recall hotels along the other station stops until Shady Grove and that's a bit of a hike from downtown. The other option here may be staying in Silver Spring, MD. It borders DC along it's very northern tip and is also on the Red Line (albeit the other side of it). There is a decently priced Comfort Inn about a half mile from the Metro. And I think there are two other hotels back there.
It's a long bike ride (solid 50 minutes or so from downtown DC), but if you rent a bike, you can also get down to Mt. Vernon, which is George Washington's home. There is a trail that runs all the way from DC to Mt. Vernon along the Potomac River and it's quite pleasant.
Let me know if you have any questions. Sometimes I wish I was unemployed, but unfortunately I will be working then.