Furnished Apartment For Rent Walk To Senate In Washington Dc . This apartment community was built in 2008 and has 12 stories with 432 units. Senate square apartments is located in washington, district of columbia in the 20002 zip code. John Jay Apartments 314 E Capitol St NE, Washington, DC, 20003 from www.realtor.com The clifton offers studio to 3 bedroom apartments ranging in size from 370 to 1441 sq.ft. Senate square | 201 i st ne, washington, dc. Most errands can be accomplished on foot in 20012 washington d.c.