Welcome to Trip Advisor and the Maine Forum, Nicole.
The Number One "must see" on most folk's list would definitely be Acadia National Park. Even Bonnie's descriptino understates just what a great destination it is. Google it for photos and information.
Depending on where you're entering the state and where you're planning to leave it, you might want to consider stops at places like The Nubble Lighthouse in York, the Perkin's Cove section in Ogunquit, Dock Square and President Bush's summer home (drive-by only) in Kennebunkport, the Old Port redeveloped district in Portland, Portland Head Light lighthouse in Cape Elizabeth (just outside Portland), the coastal town of Camden (great little harbor and waterfont with numerous day-cruise opportunities), and, to experience the less-touristed, slower paced parts of the state, consider a trip to Lubec (with Campobello Island and the summer home of Pres. Franklin Delano Roosevelt just across the bridge in Canada -- but you'll need your passport to get over-and-back) or Eastport, home of West Quoddy Head lighthouse, the easternmost point in the continental United States. The above suggestions can be Googled for photos and more information.
As far as antiquing is concerned -- you could check the Maine Antique Dealers Association website to find prospective dealers along whatever route you choose. If you're in the Central Maine area, the riverside town of Hallowell (just south of Augusta) was once the "Antiques Capital of New England": While some of the former shops have gone out of business, there are still several good shops in town.... and it's a great place to walk the brick sidewalks, poke in the numerous variety of shops along Water Street (the main drag in town), and then take a walk along the Kennebec River Rail Trail (hard-surfaced trail that runs along the river) where sightings of bald eagles and other water birds, plus river wildlife are common.
A week is probably not enough time to do "all" of the above, but if you start to narrow in on the things you really want to do, the folks on the Maine Forum can help you flesh out the details....