Historic dc hotel close to capitol hill 2 miles from smithsonian a 10 minute drive from capitol hill on the historic gallaudet university campus the kellogg conference hotel at gallaudet university is 2 miles from the national mall and smithsonian museums a 26 minute drive will take you to historic and trendy georgetown shuttle to union station you can hop on the free shuttle to dcs transportation hub union station and experience its shopping and dining options for the quintessential