Are you cruising the Eastern or the Western itinerary?
We did the Eastern in October and didn't spend much for shore excursions but we were 4 adults and did not have kids or treens along. If you want to do exciting things it is easy to spend a lot of money but in most ports there are some pretty inexpensive things to do if you do research before you go and arrange things ahead of time.
We took our 2 young kids (2 and 5) on the Western cruise in October. They have a very good Kids club on board, but you have to be 3 to get in (they check birth certificates)..one thing that I never knew before the trip is there pools on the ship are salt water. This was a dissapointment, as our kids did not really like this...As far as excursions we did not do too much as there are minimum ages for quite a few of them. I do not know what they provide for excursions as far as floaties, strollers etc, but I dont remember them telling us about any of these.
This was our first cruise, and although I am trying to stay positive I would not go on another cruise with small children again..Once the pools were out of the equasion for our non-swimming children the ship is fairly limited in activities for little ones. Coupled with the fact that excursions are limited for small children we felt ready to go home by Wednesday even though are kids are awesome travelers.
Overall we had a good time, but wish we would have been at a resort with a non salty pool and large rooms.