For sightseeing, you are best off heading south into D.C., which has more major attractions than you can shake a stick at. But if you've been there, done that, there are some off-the-beaten-path attractions in Montgomery County. There are several quite unusual destinations that can make for a good trip. The National Mormon Temple in Kensington is enormous and impressive, famously drawing comparisons to the Oz's Emerald Palace from daredevil Beltway graffiti artists. You can't go inside, but you can take pictures from the outside and learn about the temple and the Church of Latter Day Saints at its visitor center. Nearby in Forest Glen is the very weird collection of exotic buildings at the half-abandoned National Park Seminary: a Japanese pagoda, a Swiss-style castle, a Dutch windmill, etc. Glen Echo is a unique "antique amusement park," still operating a carousel, a Spanish ballroom for dance lessons and events, dramatic theater, and other attractions.
The one truly big attraction worth seeking out, though, is the imposing Great Falls on the Potomac River in the Chesapeake and Ohio Canal National Historical Park. The Maryland side boasts the best views of this massive collection of rapids and waterfalls, and makes for a great picnic. The park itself would be worth visiting even without the draw of the falls for its historic charm. For more outdoor attractions, try Wheaton's lovely Brookside Gardens.