Some mornings, when we want to catch the sunrise, we check the estimated time the night before. Then we get up early, pack a quick picnic lunch (homemade muffins, fruit, juice and tea), and head to the beach (usually New Smyrna Beach), to watch the sunrise.
When it comes to seeing the moonrise over the beach, you can easily plan that as well. We prefer to go to the beach in the evening. While there on Monday night we were leaving when a small crowd of people had gathered. They told us that in a minute the moornise was going to happen over the beach.
If you would like to plan on taking the kids to see a sunrise or moonrise over the beach, you can find the times for it each day, at this site here. Just pop in your location (Daytona Beach, New Smyrna Beach, etc.) and then the date. You'll have the times at your fingertips and can plan accordingly.
My kids have always enjoyed seeing the sunrise and moonrise. Yours just might as well!
Pictured: Top picture is a sunrise over New Smyrna Beach. Bottom is a moonrise over Daytona Beach Shores.