Heya. I'm a born and raised native Washingtonian! I can't recommend enough the Skyline Drive suggestion. Absolutely beautiful. There are actually two lodges in Skyline: Big Meadows and Skyland, so check both. I think Big Meadows closes earlier in the season because it's higher elevation. We've been there many times, both tent camping and staying at the lodge. There are a lot of cute villages in the area too like Sperryville, Lurray and Little Washington. Just north of Little Washington there is a traditional English pub, started by an American couple who lived in the UK for several years! I forgot the name, sorry.
Rehoboth Beach is another excellent place to visit, even in winter. We just came back from a weeks holiday in Rehoboth for our annual beach week. Lots of nice B&Bs and the town is very traditional and quaint unlike some of the larger nearby beach resorts. Suzanne, the restaurant in Dewey that you mentioned is actually called the Starboard. It has an amazing brunch including Crabs Delmarva: eggs benedict with lump crab meat. (As you can tell from my screenname, I'm a HUGE fan of crabs!) They also have a huge Bloody Mary bar but I prefer mimosas (Bucks Fizz, for you Brits!) Rehoboth also has a huge Christmas carnival but not sure about the dates. Next to Rehoboth is the small Dutch village of Lewes. From there, you can take the ferry to Cape May NJ. Personally, I find Rehoboth much nicer and romantic than Cape May.
Another reason to go to Rehoboth: TAX-FREE SHOPPING! Delaware is one of a handful of US states that have no sales tax. We always take an empty suitcase to Rehoboth to stock up on clothes that are a fraction of what you will pay in the UK. Rehoboth has hundreds -- HUNDREDS -- of name-brand outlet shops.
FYI: Skyline is just under 2 hours drive from Washington; Rehoboth is about 2 hours, 15 minutes, depending on Bay Bridge traffic.