A long weekend for a Texan tells me you're likely flying in.
If so, I would say fly into Portland either late on Thursday or early on Friday, rent a car, and head south to Kittery via I-95. Check out Kittery Trading Post and grab a lobster roll or fried clams at Bob's next door. When you leave, turn left out of the parking lot and head north on US Route 1.
Spend some time checking out places such as Ogunquit Beach, Wells, and Kennebunk Beach. You might consider a short cruise out around Nubble Lighthouse, which takes a couple hours.
Then, head into Portland and check out the waterfront. The Old Port is a great place to grab a drink and a bite to eat, as well as to do a bit of shopping.
From Portland, head to Cape Elizabeth and visit Portland Head Light.
Then, run up to Freeport to visit L.L. Beans before going to Bar Harbor.
Leaving Bar Harbor, head inland towards Bangor and then turn south on Route 202 towards Augusta.
From Augusta, it's a short drive back to Portland Jetport.
Alternatively, you could head north from Bangor and visit Baxter State Park before returning to Portland via I95.
Spend Friday on the seacoast in York County, Friday night in Portland, Saturday visiting Cape Elizabeth, Freeport and Bar Harbor, and Sunday visiting the interior-whether it's Bangor and Augusta or Baxter State Park and Mt. Katahdin, and fly home on Monday.