First, whatever hotel you decide is best for you, make the reservation directly with the hotel (via their web site or 800 number). Ask any hotel and they will often admit that people who make their reservations through sites like priceline.com will get a worse room than someone who booked a room through their hotel directly.
I'm a big fan of the Marriott chain and they are affordable and often have nice amenities. I highly recommend staying in the Rosslyn section of Arlington. It is just one subway stop away from the District, and Rosslyn is safe, has a small business district (with some shops and restaurants), and is on the subway line. It will get you to either the District or south to Arlington cemetary in minutes. If you are a Marriott traveler rewards person (you can sign up for free on marriott.com) then you can receive weekly emails from Marriott that provide promotional codes. You can save up to half off the rack rates.
There is a Marriott/Key Bridge and a Marriott Residence Inn, both in Arlington as well as a Courtyard (but it's on a small hill) in Rosslyn.
If you want to visit the white house over the holidays, I would contact my congressperson for tickets now because that venue is going to be swamped over the holidays because of the decorations, etc. at the white house.
I think your hardest decision will be what to visit in your two days in DC. Tailor it to what your interests are. If you like art, go to the National Gallery or the museum of american art/national portrait gallery. If you have kids that are coming with you, the Air & Space museum and the dinosaurs at the Natural History museum are big hits. If you like theatre or fine arts, go to ticketplace in the district for half price tickets for many plays and concerts. If you are a history buff, visits to the National Archives, all of the monuments, and the Capitol building.
For a museum that is tremendously moving, the Holocaust is a wonderful choice. On the other side of the spectrum, the Spy Museum is entertaining, interesting, and allows you to play spy.
If you go to the monuments, my recommendation is to go just as the sun is setting. The vietnam veterans is particularly dramatic and moving just as the sun is setting.
Hope this helps and enjoy your trip!
Source(s):
I teach a class on frugal travel. I used to live in DC and now go there frequently.