Hi there,
Getting a JR Pass would mostly depend on if you also visit Kyoto/Osaka from Nagoya (or not). Going from Tokyo - Nagoya alone is below the price of a 7 day JR Pass, however you can start making savings with a JR pass if you would visit Kyoto or Osaka.
Nagoya itself is generally not a place many tourists stay at, although there are worthwhile attractions. Such as Nagoya Castle, the science museum and train museum. At the same time it's less than an hour to travel to Kyoto or Osaka, so making a day trip (or two) makes perfect sense. Kyoto is especially nice for it's Japanese traditional character and there are some wonderful places to visit that are also fun for children. Such as the Arashiyama Bamboo groves, the endless tori gates of Fushimi Inari and the Toei Kyoto Studio Park where you can dress up as Samurai, Ninja or Geisha.
Osaka is an other metropolitan city but very much with it's own character. The Universal Studio and the local Harry Potter world are great. There's also the Osaka Aquarium that comes to mind.
Children below the age of 6 can travel for free, while children between 6-11 pay half price. Details are here:
http://www.jrpass.com/blogs/japan-rail-passes-for-children
Hope this helps,
Daniel