Find a place near a red line metro stop in Maryland (Silver Spring, Wheaton, Glenmont, Rockville, etc). From there just take the red line train to Union Station and walk to the Hyatt from there (maybe a 10 minute walk). Stations on the east side of the red line (Silver Spring, Wheaton, or Glenmont) will be closer than those further west (Rockville, Twinbrook, Shady Grove). You can look up a rail map and calculate rough travel times on
Metro's website.