There are No Hotels Near the Rockville Metro
Twinbook which is one stop away and offers a Hilton within walking distance to the Metro. Shady Grove which is the last stop on the Red line and is one stop away has a few hotel options, but none within walking distance. The Comfort Inn at Shady Grove will shuttle guests to the Metro and is one of the most preferred hotels for access to the Metro at a cut rate. The White Flint station is the last station before Bethesda and has one hotel that is within walking distance. Ride time to Bethesda from Rockville will take about 15 minutes max. Bethesda offers may hotels near the Metro.
About the Rockville Neighborhood
Rockville is NW of DC in Maryland. The area is very suburban and can be congested especially traveling along Rockville Pike. The most notable attraction to Rockville is Rockville Town Center (or Town Square). There you can find a movie theater, restaurants and shops. Accessing Reagan national from Rockville will require a long metro ride down the red line and a transfer at Metro Center. This ride will almost always take over an hour. A cab to DCA will cost over $50. BWI can be accessed by taking the MARC. Dulles is quite far. There is not a VRE stop.