Portland International Jetport (PWM) is your best choice for domestic flights into Maine.
PWM Website
For international travelers you may find better rates flying into nearby Boston Logan International Airport. From there you can either rent a car or you can book a bus ticket to be picked up right at your terminal (luggage and all!) and let the folks at Concord Coach handle the driving.
Boston Logan Website
Keep in mind Maine is a fairly rural state and while you'll have luck calling cabs/ ubers in larger population centers, a car is recommended to best experience all the state has to offer this time of year!
Hiking, Pub Crawls, Lighthouse Tours, Foodie Destinations, Scenic Drives, Leaf Peeping, Historical Sites, Maine has it all this fall!
The better Portland (we're not biased!) has everything you can imagine! More restaurants per capita than most major cities, enough craft breweries to keep the beer aficionado busy all weekend, museums of all kinds (art, history, even cryptozoology!) in a compact, walkable package. If you're interested in checking out the best of Maine on a limited timeline, a trip to Portland can't be beat!
Visit Portland Maine

Mid October in Maine is peak foliage season and the best time to take in the incredible natural beauty of the state. Below are some suggestions for sightseeing in Maine, from drives to destinations.

Fall Foliage Scenic Drives (inland and coastal)
Height of Land Scenic Overlook
Coastal Maine Botanical Gardens
Maine Lighthouse Trips
Bradbury Mountain State Park (easy hikes for the whole family)

Nosh Kitchen Bar
Duckfat
Gilbert's Chowder House 
Beckys Diner 
Slab Sicilian Street Food & Pizza (where we had our first date!)
Burnt Ends BBQ
El Pochos Mexican Grill
Brickyard Hollow (multiple locations)
Lobster Shack at Two Lights State Park 
The Holy Doughnut



Foulmouthed Brewing
Maine Craft Distilling
Coffee By Design
Baxter Brewing Co.

Bissell Brothers Brewing
Blyth & Burrows
Flight Deck Brewing
Bramhall
Side by Each Brewing

Shopping:
Freeport (outlet heaven)
Portland (boutiques, local artisans)

Places to Visit:
Belfast, ME
Rangeley Lakes Region
Portland, ME 
Acadia National Park