The ferry to Green Turtle leaves from Treasure Cay, about an hour north of Marsh Harbour. If you want to spend time on GTC, I would check into accommodations there, it's probably going to be a nicer few days than being in MH, though I don't know for sure as I've never spent more than a night in Marsh Harbour.
If you stay in MH and you're a boater, renting a boat is a great way to explore the Cays, each with some unique offerings. If not, most of the other ferries leave from the Marsh Harbour area, and can get you over to Elbow Cay, Man-O-War Cay, or Guana Cay for the day. Elbow and Guana are the more tourist friendly cays with shops and restaurants, where as Man-O-War is a quieter pace. Unless you're a confident boater with ocean experience in an outboard boat, I wouldn't recommend taking a rental boat from Marsh Harbour up to Green Turtle though as running inside of Whale Cay can require navigating shifting shoals while heading outside puts you on the Atlantic.
If renting a car, Great Abaco has a national park all the way down south with some rugged hiking for the adventurous, and if you're a birder a native population of parrots which actually nest underground. Heading south you can hit up Nancy's restaurant in Sandy Point, and look out on Castaway Cay, the Disney Cruise island, while drinking a cold beer and eating one of a very limited number of menu options knowing they'll all be stellar, though I've questioned the compliance with fishing regulations. One of my favorite things to do is paddle board in the mangroves around Wilson City and Snake Cay, I *think* there is still someone doing tours post covid/Dorian, but don't know for sure as I just run down in the boat with my boards.
When in Abaco, be sure to buy the locally produced chicken, Abaco Big Bird - it's fantastic, organic fed, hormone and steroid free, and the people who own the farm properly work their butts off to compete against the imported crap we call chicken in the USA. They also make homemade ice cream, produce some fruits, and do takeaway food. And never skip out on stopping for conch salad along the roadside.
