We did an Alaska cruise in 2002 on the Sky we had a JJ interior superior cabin (I don't know what category the interior superior cabins start) but it was very roomy for 2 of us, now depending on the age of your children and the amount of time you plan on spending in the cabin it might be OK. The cabin had two twin beds put together to make one and had two bunk type fold down bed hanging off the side walls, one on each side. With the bed together you had about a foot and half on each side of the bed and with the fold down bed above it was a little tight going down the side of the bed. We have them move the beds apart leaving about three feet between the beds and easy access to the upper beds. This works if you don't mind sleeping in separate beds for a week, it made the room seem a little more roomy to us. It had a couch and a small sitting table under the TV. Most of the interior rooms in the same category are close to the same size just on different decks. The interior cabins are dark so maybe you can bring a night with you. You can go to ncl.com go to the ships and find info on the Sky. You can talk to your TA and they might have some more input. As for the food it was very good then but everyone has different taste and it was six years ago, maybe someone who has just gotten off the Sky can help more with the food. As for the ports we have not been to them yet.
Enjoy your cruise