Mornings are great at the beach, specially if you have children. The water is calm and warm. A short 12 minute drive and you have your feet in the sand. We love Sebastian Beach. Public parking is easy and affordable and there's plenty of shops, cafes and restaurants (not to mention Starbucks).
Can't be bothered to pack a beach umbrella? your private outdoor retreat comes with a grill, plenty of lounge/sitting/reading/napping/sun bathing spots. Grab a chill drink and soak in the warm pool water.