Ahoy, Amy!
A birthday is the perfect reason to take your family's first Disney Cruise Line vacation (although, I believe a Tuesday is a good reason to take a cruise, too!).
Whenever I am booking a cruise, I look for a stateroom that is located midship. I like to be centrally located and just about the same distance from the theater and the buffets! I also look for a stateroom that is NOT directly in line with the elevator. Sometimes, late at night, people forget their manners when exiting the elevators.
If I am going a cruise that docks at Disney's Private Island,
Castaway Cay, then I definitely recommend a stateroom with a porthole or verandah on the starboard side of the ship (that's the right to all non-sailors). This is the side that has the view of the Castaway Beach and the majority of the island. If you are on the Disney Dream or Disney Fantasy, there are virtual portholes in the inside staterooms that will also give great views of Castaway Cay.
I also try to look for a stateroom that is "sandwiched" between other staterooms. This means I don't want the theater or night club below me or the pool deck above me. I find that the quietest rooms are the ones where there is a stateroom both above and below mine. I once made the mistake on another cruise line of having my room directly under the pool deck, where they began moving deck chairs around 5am, making sleep impossible!
I hope this helps planning your first Disney Cruise! Please come back and visit the Disney Parks Moms Panel with further questions or to do some research as you are planning.
Happy Cruising, Tracy V.