The Keys aren't really known for their fantastic beaches but there is a fairly nice public beach in Key West. Don't worry about the water, it is fine. Some of the hotels advertise that they have beaches but they are generally very, very small patches of sand and none on the gulf side. I'd suggest renting a car for at least a day and driving up to Bahia Honda State Park. That is probably the prettiest beach in all of the keys.

We stayed at the Hyatt the last time we were there and it was very nice ... spectacular views ... but the pool area was small. The Wyndham Casa Marina is probably one of the nicest properties on the island with a beautiful pool area.

The weather will be beautiful in June. I lived in the Keys and I loved the summer there. We spend every Memorial Day weekend in Key West.