First of all all Europe is about 40% higher cost when the US excluding Alaska.
Set you budget first and then determine if the grand parents and children are interested in specific activities on shore.
The caribbean is the most competitive, Alaska is a good call.
Depending on the geographics, flying is a major expense.
The onboard activities on the major cruise lines vary, Carnival, Princess, Royal Caribbean, NCL, Celebrity are your best choices. they all have children/teen ager programs.
Royal Caribbean have smaller cabins. Princess has 24 hour buffets and compete in pricing with Carnival with has large cabins.
Celebrity has more class and better food in the dining rooms, the grand parents will enjoy.
NCL has the lowest prices generally speaking but the extra charges after boarding will suprise you on all the cruise lines. Soda cards, coffee cards, tips, ect.
You can e-mail me if you want to learn more about cutting cost @ firstname.lastname@example.org
Make sure you place cruise ship on the subject line.