Timing is more important than ship when considering "family-oriented" cruising. Avoid spring break, summer break, and Christmas at all costs. I recommend sailing between September 1 and Thanksgiving or between January 1 and March 1. These times are the least expensive times to cruise (with September being absolutely cheapest) and with the fewest children aboard. The ships are also just generally less crowded with many fewer people sailing as thirds and fourths in a cabin.

If you have an idea of where you want to go, I could offer a recommendation or two. Stick to 7 night or shorter cruises for good nightlife. One recommendation I can make off the bat is Carnival Legend out of Tampa. It usually goes to Cozumel, Grand Cayman, Belize, and Costa Maya, though Belize and Costa Maya are temporarily off the itinerary due to aftermath of Hurricane Dean. Belize should be back on in a few weeks. Cozumel is my favorite Caribbean port, though, and Carnival Legend is one of the Spirit-class of Carnival ships which has the highest space to passenger ratio. The Port of Tampa is also fantastically efficient, the airport is cheap and easy to fly to from anywhere and is a $20 cab ride from the Port.

Check out Cruise Critic for more info as well. Once you pick a ship and a specific sailing that is best for you, use Cruise Compete to find a nice deal.