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The open air market is one of them, its open 24 hours a day except for Sunday nights and it includes fresh fruit, vegetables and various other wares that the people of Santo bring to the markets from their village gardens. You can't beat the quality of their produce as it's all organic and incredibly cheap.
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Go to the outdoor produce market in the western end of town and buy some of the organic fruit and vegetables.
Take a walk up to the top of the big hill and enjoy the view of Sagond Channel and Aore Island.
The biggest draw to the island is the wreck of the SS President Coolidge, a World War II troop carrier sunk by friendly mines in 1942. The majority of people travelling to Santo are divers who come for the expressed purpose of exploring this famous wreck. As such, there aren't many things to do in town other than to visit the local dive shops and organize some diving. Aquamarine is on the road opposite of the Unity Shell station and features a friendly and very experienced staff. They can take care of all your equipment needs and boast wide variety of Padi certified scuba courses at very competitive rates.
There is a golf course on Santo and if you meet up with some of the local expatriates they can give you a rundown of when the best times to go and play are (and if you make a good impression they may even let you know where you can borrow some clubs)!