Train
When not hailing a taxi/lyft/uber or walking, the metro is a great way to get around. The website lets you plan your trip so you know which trains to take. Most museums and sights to see are within walking distance of a metro station.
Hotel
Washinton, DC has a plethora of hotels, more than we could ever list. We recommend staying in the West End neighborhood (which is about a 15-minute walk to the reception and next to many restaurants). Dupont Circle is also close and a nice area to stay in. Below are some hotel options we recommend. Please feel free to stay elsewhere based on your likes/preferences. As our party is small, we did not do a hotel block, thinking you would prefer to find a hotel to best fit your needs.
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Farther away, outside pool.
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If you wish to stay in Rockville instead of DC, this is the hotel for you. It is walking distance to the Rockville Metro station, great Chinese restaurants, and close to the ceremony and Christine's parents' home.