Larry,

Romer Shoal is a New York Lighthouse. It may be physically closer to land on the NJ side, but it's a NY Lighthouse.

As for Great Beds the best I can tell you is that the sources I can find consider it a NJ Lighthouse. there are very few sources with any info on this Lighthouse. It's ownership was debated in 1880 and it was decided that it was in NJ.(Source National Lighthouse museum Site)

The National Park Service site lists it as a NY Lighthouse, but mentions the fact that some sources place it in NJ. I'd say to be safe, youd have to mention the debate.

I know this doesn't help completely, but it's the best I can offer.

Dennis