Fitts Village is as folks here have said nice combination of being on the west coast with the great beaches while being out of the way enough from the Holetown area to be able to have comparably lower pricing. It is a more local area and does have a supermarket close. In terms of dining, Il Tempio is a nice little Italian place on the beach within walking distance, and you are not far from Cin Cin and the Cliff, or the restaurant at the Waves hotel whose name I cant remember now.
Baker's Woods is def not a holiday area, and you will need a car if you want to get the most from that area, it's at the top of the hill from Mullins Beach and I would describe it as a hike rather than a walk should decide to attempt it. Shops and restaurants are not close at all.
Sunset Crest is smack dab in the middle of the Holetown area, so you could get away without a car but may pay a premium for its location.