We had a great experience at Sea Garden Cottage. The place is typically Caribbean, there is a lot of vegetation around the house which makes you feel you are in the middle of a tropical garden. There is a pool shared by 3 properties but there is always space. On the inside you have a nice kitchen and good AC. The shower is not great but you can manage.
Also there is a mobile line in the house but you will have to buy your own credit.

The neighborhood is nice a bit of a walk/bike ride from where the 'buzz' is or where the ocean is. So you have to walk to the doc (not far away). We didn't even go in the end so that could be a negative if you want to chill by the beach.
The island is very small and the vibe is very chilled out, relaxed with great restaurants and bars. Sea Garden is 6-7 min by bike from the restaurants/water taxi area.
If you are looking for a secluded space with great pool and garden this is the place for you :)