There also a Wynn Dixie, both Publix and Wynn are on US 1(Roosevelt) as your going into town on the island. If you never had been the madness at sunset at Malory square is to be experienced. The Hemingway house is on whitehead street, along with the iconic "beginning and end" of the highway markers. Also at the southern end of whitehead is the "southern most point" buoy, there is always a line and people to help take a picture of the both of you. There is the butterfly house close by the southern most point also. If you like history, there is Ft. Zachery there is also a beach at the park, you pay to get in but it is good for all day, you can come back and see the sunset from probably the most unobstructed view standing on the island.
Check out El peps(spelling) for authentic Cuban food try the Cuban coffee is you need a wake up, and they have live music, right at Mallory square. There is also Smatters beach just a short ways from Windward, but being on the Atlantic side some times it's has sea weed washed up on it and the trades blowing in make it cooler. You might to try Hog fish bar and grill on Stock island, great sea food, thats the last island just as you're going over the bridge to Key West. There is also Roosticas on stock, great pizza.
There is so much to see and do you can't it all down in writing, check the front desk for some ideas. Have fun.........