The Capital Region is the most densely populated region of the state, home to the most populated Washington, D.C. suburbs, and satellite cities worth visiting, such as Bethesda, Gaithersburg, College Park, Silver Spring, Kensington, and Rockville. Rock Creek National Park is another reason why you would find yourself here—the long bike/running trail is great. Much of it, though, is suburban sprawl that has covered all the once beautiful Piedmont Plateau, and does not constitute any kind of tourist attraction, although plenty visit on business.
Frederick County, while still in the capital's orbit, has a more rural character, as do northern parts of Montgomery County and southern parts of Prince George's County.
The main interstates leading into the Capital Region are I-270, which cuts northwest through Montgomery County and continues north to Frederick, I-95, which goes north through Prince George's County to Baltimore, and, of course, the Beltway (I-495), which runs east-west across Montgomery and Prince George's Counties as it circles around Washington, D.C..
From D.C., the main roads leading north into the Maryland Capital Region are (in addition to those listed above) Wisconsin Ave, Connecticut Ave, Georgia Ave—all of which lead into the wealthy and densely populated suburbs of Montgomery County.
The Beltway and its main arteries (I-270 and I-95) are the best way to travel between the three counties of the Capital Region. I-270 is a very convenient highway for traveling between Montgomery and Frederick Counties, and there's really no better way to go between the two. Unfortunately, there is an odd lack of east west routes other than the Beltway, which lends to the extreme congestion between Prince George's and Montgomery Counties (and the extreme ire that engenders in the hapless, motionless drivers).
Many drivers unaccustomed to the Beltway find its banked curves with traffic going 65-75 miles per hour with little to no space between cars alarming and unpleasant to terrifying. A good tip for avoiding the Beltway in moving between PG and Montgomery Counties is to take the East-West Highway instead.
The fabled Purple Line, which would mimic the Beltway in connecting the suburban areas to one another, is always under proposition and discussion, but may never come to light in the face of fierce opposition by homeowners that it would displace. So to connect by rail between PG and Montgomery Counties, you have to take the Red Line all the way into downtown D.C. to transfer to the Green Line. Just to go from Bethesda to Silver Spring (which are practically adjacent), you would have to ride for an hour through D.C. on the Red Line.
So take buses instead if you are using public transport. The bus system is quite good and comprehensive. Use the county Ride On buses to go from point to point within Montgomery County, and the WMATA metro buses in traveling in between the two inner counties.
In general, the Maryland Capital Region is not the type of place you visit for sightseeing—you visit it to see family, or on business, since it is a huge commercial and residential center. But there are a few odd sights to find off the beaten path. The largest is the Emerald Palace-like National LDS Temple in Kensington, which boasts a spectacular display of Christmas lights and nativity scenes during Advent every year. NASA's visitor center in Greenbelt is another great reason to venture forth from Washington, D.C. for a Maryland attraction. Perhaps the most important sight, though, is Great Falls in Montgomery County along the C&O Canal on the Potomac River. You'll be surprised by how big and impressive the falls are, and the Maryland side is great for viewing them—you get to walk out along a long bridge to an island in the middle of the river.
Also consider hiking up '''Sugarloaf Mountain''', located in Dickerson, Maryland. It's a popular local destination for hiking and picnicking. Although the land is privately owned, it is open to the public and no entrance fee is charged.
Bethesda has many top-notch restaurants, serving all the suburbanites who converge upon the small city nightly. For a cheaper and less crowded experience, look for some of the great ethnic restaurants in southern Silver Spring and in College Park. The Route 193 "International Corridor" near Takoma Park has a variety of immigrant-fueled cuisine -- everything from Indian to Peruvian. Alas, much of the rest of the region has fallen victim to endless strip malls full of middle of the road chain restaurants.