We sailed the Zenith to Bermuda in 1999 & she's a great ship. I think of the four ships sailing from New York, the Horizon or Zenith are the best choice, but I'm partial to Celebrity. I understand that Bermuda has a street fair in Hamilton on Wednesday nights during the summer months and I think that Horizon is in Hamilton on Wednesdays. Though we've never sailed on Horizon, she's almost identical to Zenith except she doesn't have hot tubs.
I agree that Bermuda is the best seven day cruise. The island is immaculate and the people are the friendliest and the beaches are the best.
New York City is the most beautiful port to sail from, with the skyline and the Statue of Liberty in the harbor. I'm sure it's even more emotional with the absence of the World Trade Towers.
Hope you and your parents enjoy your cruise!!