is there a grocery store nearby for basics?

There are two groceries on Sanibel, Jerry's and Bailey's. Unlike other beach resorts, Sundial has a Bailey satellite. Make sure you stock up before you cross the bridge however. I recommend Aldi's and Publix at the San Carlos intersection.

Bailey's is close

There is a small market inside the complex that also makes coffees and sandwiches. There are 2 markets less than 3 miles away.

Jerry's get some cinnamon bread

Yes there is...