You're asking for something that doesn't exist. Where are you looking to stay? In DC or in a nearby community with a shul?
Silver Spring may have something like that; not sure how close it is to DC; also start with with Godaven.
Find a hotel in the general area that you want and then check with Godaven to see how far it is from a shul or do the opposite if you already know of shul you want to stay by.
No clue how far by public transit this is to DC but here is an idea to start with with
Name: Young Israel Shomrai Emunah of Greater Washington
Address: 1132 Arcola Ave, Silver Spring, MD 20902