Ride in to Sandy Hook and drive to the far parking lot near Officers' Row. Park there and ride all you want
Mind the hikers and joggers
I would take JerseyJack's approach and drive all the way in, then bike out as far as you want to go. My husband and I did that once, and it was very nice.
If you haven't left yet: I would drive into Sandy Hook, park just after the toll booths, bike all the way to the end and enjoy the views by the lighthouse, bike back to my car. Head to Atlantic Highlands (don't know anything about Sea Bright) and eat at the Inlet Cafe, on the deck. http://www.inletcafe.com
It can be very windy there. If possible, plan your trip so you head out into the wind and return with a tail wind.
Park in Atlantic Highlands (Follow signs for the Henry Hudson Trail. Plenty of free parking there) and bike over the bridge to Sandy Hook.
This gives you free parking, a longer ride and plenty of good options for lunch/dinner when you return.
Here was my route from "MapyMyRide" earlier this season: http://www.mapmyride.com/workout/1018614501
You can also start your ride in Sea Bright, but parking is a bigger challenge there.
We wanted to take our bikes to Sandy Hook tomorrow for some bike riding. Some suggest parking in the towns next to Sandy Hook and riding bikes in. Does the bike trail start as early as Sea Bright? Can we take the trail from there into Sandy Hook? We thought we'd then maybe grab lunch in Sea Bright after our ride - any recommendations for casual places to grab lunch? Any information/recommendations about bike riding in and around Sandy Hook would be great. Thank you!