If you are on a very tight budget, avoid the specialtiy restaurants that you pay extra. On many ships, there are many free speciality or alternative restaurants to choose from.
You can also book shore excursions privately in advance, or once you arrive at the dock and save lots of money.
What's the best tour for your kids? I don't know. I suggest asking them what they would prefer. Use the NCL shore excursion list for ideas what's available, check them out over the world wide web, then book them.