I suggest a Western Caribbean on Royal Caribbean or Carnival. A seven day cruise will give them time to enjoy their honeymoon plus enjoy the beaches and activities, and water of the Caribbean Islands.
The Radiance class of Royal Caribbean are some of the most beautiful ships at sea. The Voyager and Freedom class of ships on Royal Caribbean have activities that will fulfill the most active to those who just want time to themselves.
Carnival will give them fun and great food plus larger ships with a wide variety of activities.
All of these ships and cruises can be done at a fairly reasonable price. Check around with some agents and see what you come up with.
I personally feel Bermuda may be a bit laid back for them but if they want something more laid back then that is OK but they will spend more money on shore and use the ship as a "floating" hotel.