Flight
I highly recommend flying into Reagan airport if you're flying. It is a smaller airport than BWI or Dulles and located 4 miles from the city center. There is a metro stop (red line) at the airport that can take you pretty much anywhere in the city. Uber and Left are also allowed to pick up passengers from the airport. Also, Southwest offers service from this airport.
Hotel
Located in the newly-renovated Wharf area about 1.5 miles from the reception venue, District Winery, this is a beautiful new modern hotel. They offer shuttle service to and from the nearest metro stop. Early booking rates $189/night for standard room
Hotel
Located in the newly-renovated Wharf area about 1.5 miles from the reception venue, District Winery, this is a beautiful contemporary hotel. The hotel is set to open in September, 2017. Hilton member rates are $151/standard room.
Hotel
This is a classic DC hotel located in the heart of DC, Dupont Circle, with a rooftop bar that has bragging rights to views of the Washington Monument. They also have a spa. Current rates are deals at $209/night but they won't last long.
Travel Note
There are tons of great air b&b places to stay in the DC area. If a hotel isn't for you then check out the website to see what is available and may suit your needs for the weekend.