The Fish Bay area is almost the end of the South Shore road. The good news is that the road is all paved now. There is a good bit of construction since I last visited. Check with the Villa Management or Owner to find out if there is any construction in your villa's immediate area. If there is it might wake you up around 8 but work usually ends about 3pm.
The bay itself I snorkeled in many years ago. I doubt much has changed. It can be very calm water when the wind is from the north. Not much to see if you are only into reef and rocks and pretty fish. However, if you would like to see rays and eels you might be pleasantly suprised. Unfortunately my wife wasn't into that and we had to leave at the first eel sighting. : (
The drive to the grocery is essentially the same as the drive into Cruz Bay. Expect at least 15 minutes. Sometimes you can make it in 10 but who is in a hurry? We used Starfish Market. They were closest and best supplied and priced.
To the North Shore add another 15 minutes (Lets use Hawksnest as a gauge). Again, who is in a hurry.
To the get to the Coral Bay side you can bypass Cruz Bay with Gift Hill Road. VERY winding and steep but worth the drive to avoid town especially around 3pm (school lets out and shift change at the Westin I think.)
If your into quiet private beaches and don't mind a short hike, drive to Reef Bay and park near the cedar shingled roof house. (Slimans) Climb down the hill and find a spot on the mile long beach that very few visit. If you are very adventurous, you can walk the beach to Reef Bay trail and hike up to the Petroglyph pool. Check the tidal charts first as there are two rock scrambles on the way that are hard to negotiate at high tide.