The Old Port and surrounding neighborhoods are full of unique shops, dining and drinking options. Novare Res is a personal favorite of ours, with an amazing selection of local and Belgian beer and an outdoor patio. Make sure to grab something sweet at The Holy Donut, too!
Check out the local arts and music scene: if you arrive early, there is a First Friday Art Walk of galleries around the neighborhood, free weekend admission to the Portland Museum of Art (Bank of America cardholders), live music at Port City Music Hall and local bars, or even burlesque competition finals (on Saturday night)!
Good god, we don't even know where to tell you to start here. Portland is a foodie destination, and there are SO MANY great places. The link provided will break it down and give you guidance, depending on what you're into. (It's not on here yet, but Highroller Lobster has a new brick and mortar downtown near city hall that is excellent for a lobster roll fix...we went after getting our license!)
There are several lighthouses around Portland and Cape Elizabeth. Bug Light is a great place to start a tour, by car or bike. Also consider checking out nearby Spring Point Ledge lighthouse and Two Lights State Park.
If there is any brewery you MUST visit, it's Allagash Brewing Company. Allagash has been around a long time, and is widely loved by craft beer drinkers (and Barry and myself). Their taproom is comfortable and inviting, and check out their website and sign up for a free tour if there are still slots left! While you're in the area, a few other small breweries are located in the industrial park across the street.