Hi Mike,
I have been to all that you mentioned.
Yes, it is possible to see them all, from Sandy Hook to Cape May, in one day. It will be a very long day, however, and you might run into problems with opening and closing times for those you can climb. You may wish to spend one night in Atlantic City or Cape May perhaps, before going home.
It is possible to drive from Sandy Hook to Cape May in about 2 hours without stopping. I usually allow 45 minutes to an hour per lighthouse on such trips (some will be much less -- If Sea Girt is not open to the public that day, you can see all there is to see in about 5 minutes.) Multiply that times 7 major lighthouses on the route (Sandy Hook, Navesink, Sea Girt, Barnegat, Absecon, Hereford Inlet, Cape May.) Add time for meals, etc., and you get a very long day. Click the link below to see other recent discussions on NJ lights. It includes other links that you might find useful:
http://www.lighthousekeepers.com/forums/Forum5/HTML/000076.html Have a nice trip.
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-Art