Grand Cayman beach break on your own--suggestions

[havaneselover]

We will be in Grand Cayman the day after Easter. I would love to find somewhere on/near the beach to have a nice lunch and then head to the beach (7 mile) for a few hours for the children to play. If I could find one place where we can have a nice/child-friendly lunch and then move to some lounge chairs that would be ideal. I'm planning on taking a cab to and from wherever we go. Any recommendations? The more specific, the better. Thanks!