My husband and I spent three nights at Atlantis before traveling to Stocking Island. What a different experience! The flight to Exuma airport and taxi to Georgetown are easy. We stopped at Exuma Market for groceries and a nearby liquor store before making the trip to Stocking Island. I highly recommend doing this. The water taxi service is easy from Government Dock (we were there around 11AM), and our driver had no issue locating Kevalli House. The manager Norman met us and was very helpful throughout our stay.
The island is peaceful and very secluded. There are other guests and people docked in the harbour, but the beach was often "just ours". This isn't a luxury property, but the house is unique and impressive. Two king beds and very comfortable sheets and pillows were a treat. There are also two bathrooms and two additional twin beds. We made several meals ourselves on the outdoor grill (screened in porch is great at night due to mosquitoes).
Things to do: relax on your porch which is harbour side (sunset side). 5 minute walk to the Atlantic beach side (images of the ocean are 5 min walk away, images of harbour are right off your house). It was VERY windy during our stay, so we found the beach better than the gazebo which was just a wind tunnel. Bring flashlights if you want to check out the ocean at night (stars everywhere!) Get a hiking map from Georgetown or download. Paths are semi-marked but I'd label them as a more adventurous hike versus easy. Kevalli House provides kayaks, snorkel gear, and flippers. The Blue Hole is right off the house (people come from all over for this, so it was very cool to have right by us). Norman can take you into town if you want to book any other tours/trips or rent a boat from Minns. Everyone is very helpful, so don't let the boat ride to and from Georgetown keep you from booking this place!
Meals out: Sunset kept us eating a bit earlier than usual. We went to the Pig Roast at Chat N Chill. This is a kayak ride away or a hike. BLU at Lumina Point is also a kayak ride away or a longer hike down the beach and past the mangroves. We opted for a late lunch - open 11AM-4PM and then reopens at 6PM for dinner.