I stayed at RWI last May and am returning again this May. There is a shuttle from RWI to the grocery store that costs $20. IGA is open seven days a week 7am - 10pm. No liquor sales at IGA on Sundays.
The Gecko Shuttle does not go to the grocery store. It runs all along the resort/beach area from Ocean Club down to Turtle Cove. Check it out at
www.thegeckotc.com. You can buy a 7 day pass for $33/person. There are also family rates. I think in June it would not be busy and you should be able to catch it every 15 - 30 minutes, depending on where you go. There is a restaurant, Mango Reef, at RWI. Had a few meals there, but remember you are on island time so service may be slower than you expect.
Also pack light, as the units have washer and dryer so you can do laundry.
Dress is very casual.
There are Hobie cats (sailboats) and kayaks at the beach at RWI and there are bicycles available. All are free to use. You can book excursions through the activities desk at the beach, or call somewhere else.
TikiHut in Turtle Cove has $10 chicken and ribs on Wednesday night, also $15.00 buckets of beer.
We did not rent a car last year, and may rent a car or scooters for one day just to explore, otherwise we will take the Gecko Shuttle as taxis were expensive to take everywhere.
Also good snorkeling in front of Coral Gardens.
You will love RWI and the wonderful beach right there. Building 1 is great and good view for sunsets. Did you go through VRBO? I know of three units in that building that save you money over the resort cost.
Have a great trip! I will try to post a report after my May trip.