which island is easily accessible from u.s. east coast for about 5 or 6 days. nice hotel, beaches. if possible some nightlife.

Aruba

It would help if you were a little more specific as to which city on the east coast you are flying from since east coast can mean anywhere from Maine to Florida. That said, you should be able to reach the following islands non-stop from most major east coast hubs: Bermuda, Grand Caymen, Nassau, Provo (T&C), Puerto Rico, Dominican Republic, Jamacia, St. Thomas, St. Martin, St. Lucia, Barbados, Aruba, Antigua.

I'm in NY

All of those islands are available non-stop From NY (JFK, LGA or EWR) which meets your definition of being easily accessible. All have good beaches, nice hotels and various levels of night life. Each island, however, offers a very different experience. You'll need to let us know more about your likes, dislikes, expectations, budget, time of year, etc. before any meaningful recommendations can be made.