Western Maryland, also known as the state's panhandle, is the most remote section of Maryland, and most popular among tourists for its mountainous natural beauty. Culturally, if the Eastern Shore is Southern, and Central Maryland more of a transition zone, Western Maryland is decidedly Northern, with a strong economic history of mining.
Hagerstown is home to the one small regional airport with flights from BWI, but a car is a far, far more common mode of transport, especially as you will need one once you arrive!
Amtrak has daily trains to Hagerstown and Cumberland from Washington, D.C. The MARC Brunswick Line  from Washington, D.C. is nice and cheap, but will only take you as far as Brunswick in Washington County. It only runs on the weekdays, catering to commuters.
To get around much anywhere in Western Maryland, you will need a car, and a car is a fine way to arrive. I-68 is the main east-west highway, running from Hagerstown and the junction with I-70 in the east (which is the highway in from Baltimore and Washington, D.C.) and from Morgantown, West Virginia, in the west. North-south routes are mostly smaller, although from Hagerstown, you can take I-70 to Pittsburgh or I-81 towards Harrisburg. US-220 connects Cumberland with I-70 in the north towards Pittsburgh, and also leads south through some incredibly beautiful and remote landscapes in West Virginia.
Aside from all the beautiful scenery, Western Maryland is certainly not a big sightseeing destination. Antietam National Battlefield, site of the bloodiest battle in Civil War History, is likely the most visited traditional "attraction." Cumberland's historic downtown is also a quite beautiful place for a walk, where you can also pick up the Western Maryland Scenic Railroad, which will lazily take you through the mountains to Frostburg, a charming old town in its own right. For something a bit more offbeat, you'll see Noah's Ark being rebuilt along I-68 between Cumberland and Frostburg. The beautiful Crystal Grottoes Caverns and the original Washington Monument at Boonsboro are another good bet for a half day activity, and are within an easy drive of Antietam.
Outdoor activities are plentiful in this beautiful and sparsely-populated region. The most famous destinations are, naturally, Deep Creek Lake and the Appalachian Trail. The former is an artificial lake in the mountains, and a popular holiday spot among Marylanders, with nearby skiing, fishing, boating, etc. The Appalachian Trail in Maryland is short, as it cuts across a very narrow section of the panhandle, but it's home to Annapolis Rock in the north--a great place for rock climbing, hang gliding, or just watching the sunset. Swallow Falls State Park is arguably the most beautiful park in Western Maryland, and a great place for hiking, camping, and of course seeing the various waterfalls!
No culinary specialties in this part of the state, and actually, there are not too many restaurants either! The best range of options will be found in the Deep Creek Lake area, along with the two main cities of Hagerstown and Cumberland. Frostburg also has a decent enough selection to feed the university crowd.