There should be loads of Korean travel agencies in NYC offering Jeju package tours. It's the number one holiday destination in Korea by far and you have something like 20 daily scheduled flights there from Seoul alone. I think a good start would be to contact the KNTO office in NYC (Ok, NJ ) at:

Korean National Tourism Office

Address
Two Executive Drive, Suite 750, Fort Lee, New Jersey 07024, U.S.A.

• Tel
(201) 585-0909

• Fax
(201) 585-9041

• Toll Free
1-800-TOUR-KOR(EA)

• E-mail
[email protected]

Jeju has many things on offer: Sandy beaches in the south where the aforementioned resort hotels are located, the Mt. Halla National Park in the centre, caves to explore, folklore villages, the world class Nine Bridges golf course, really fresh seafood all over the Island...

One thing I have enjoyed in Korea is to book a taxi for a sightseeing tour for a set fee. The concierge at your hotel can surely arrange this and you just arrange meeting point and time with the driver at each location. Jeju has decent public transport but mainly between Jeju city and the resorts on the southern coastline.

Please do remember that there are also direct flights at least from Osaka, Tokyo, Beijing, Shanghai and Hongkong to Jeju. It's not necessary to fly to Seoul first to get there.