We were just in DC a month ago and stayed at the Hilton Garden Inn Downtown on 14th St, just across the street from the McPherson Square Metro Station. It was a few blocks to the White House and we used the Metro to get us started anywhere else. HGI Downtown is nice, has a friendly staff and has valet parking (expensive, as are most of the parking garages around there, but there isn't much of a choice in the area). They offer a nice buffet breakfast, but it's expensive, so we just walked to Starbucks a block or so away and grabbed breakfast before hopping on the Metro. Oh, and you'd need 2 rooms. Our room had two double beds and no couch or room for a rollaway bed.
As far as the Metro pricing goes, something we didn't know until we went to buy tickets, is that you need to add additional money beyond the fare to each paper ticket (as opposed to a reloadable SmarTrip card which can be ordered ahead of time and has a one-time $5 fee). For example, from McPherson Square (blue & orange rail lines) to the Smithsonian stop (also blue & orange lines) costs $2.10 (off peak, such as weekends) plus an additional $1 paper ticket fee for a total of $3.10 per person from McPherson to Smithsonian, one way. If you're gong to ride a lot, it would make sense to buy the SmarTrip card ahead of time so you're ready to hop on the Metro when you're ready. You can trade in paper tickets with money left on them when you buy your next ticket as well. In our experience (off peak, weekends in May), the Metro rail was right on time, but I'm not sure how the schedule is during the holidays.