We did the 7 days RCCL western Mediterranean cruise in 09 as a family trip for my parents' 50th anniversary. RCCL was a nice ship for younger children for I had nephews and nieces under 6 and they seemed to be preoccupied.
However, Mediterranean cruising during the summer months can be hot and humid. There is also quite a long ride from port to the central part of cities.
I also made the mistake of "this might my my family's last trip together to some of these places" and not pacing ourselves. So every day it was: grab buffet breakfast and load up the backpack with snack and liquid, get off the ship for excursion, rush back post excursion and clean/dress up for family dinner during the early seating (24 of us), immediately to bed so we can repeat the routine for the next day.