Another great area to visit is Kamakura and Enoshima (can do as a day trip from Tokyo)........
........ Toyota museum/tours ..........
We also loved Takayama
Just seconding some of these comments.
The Kamakura/Enoshima/Ofuna triangle are great. We were happily able to spend a full three days non-stop there without any trouble. You can get the Narita Express direct to Ofuna (train splits in two at Tokyo station so make sure you are in the right half). We stayed in Ofuna (JR-EAST hotel next to the station was good value) as we found it to be most practical for transport and food options for what we wanted to do. It's a good way of avoiding the hustle and bustle of Tokyo on arrival. Various local passes available for transport. Kamakura Enoshima pass (JR) ¥700/day was useful. National parks in the area are beautiful if you like hiking (locals will discourage you from taking the more adventurous trails because they seem to think we are a bit soft - when they saw decent hiking shoes they were more understanding though I would take walking poles next time as Japanese ideas of OH&S on these trails are a bit less than we might see in Aus.) Black sand beaches around Enoshima were interesting as well. Staying at Ofuna also makes access to Yokohama quick and easy, or our favourite, the Kirin Brewery tour just on the other side of Yokohama. Tour is in Japanese but you get headsets with English translation and very attentive guides. Once again, lots of fun and the tasting samples at the end of the tour are 3x500ml beers, so get there by public transport!
I was going to say if you weren't going to Nagoya you could still soak up everything Toyota at the Mega Web Toyota City Showcase in Odaiba area of Tokyo, but when looking up details just now, it shut down at the end of last year. We went there ourselves because we had a day of torrential rain, not expecting much, but we had a great time spending far more time than we thought. Supposedly they are moving the exhibits to a new, as yet undisclosed location.
Takayama is also great, including the train journey from Nagoya. There is a historical village attraction walking distance from town that we visited with children of various ages that all really enjoyed. If you are looking for gifts, the Takayama Sarubobo monkey baby dolls are great. They have no faces. The idea being that can then have whatever expression or emotion that is appropriate (or at least that is what I was told).
Other thoughts:
If you like train journeys, try one of the "resort trains" or "Joyful trains". We did the Resort Shirakami from Akita to Aomori along the north west coast of Honshu and it was well worth the effort.
We also liked the Hakone region. Once again, lots to do, especially if you like hiking, but lots of other options too. We did the full Japanese accommodation experience here. "Half board" so full Japanese style multi-course breakfast and dinner with all the local specialties. For dinner you were expected to dress in full Japanese style (all supplied) which we did (it was fun), but the one other pair of foreigners staying there who didn't want to do that were accommodated without fuss. We stayed two nights and dinner and breakfast was different each day, with all the local seasonal specialties. When we expressed interest in what we were eating, the Maitre'd would laboriously type into Google Translate and present us with the results. He seemed genuinely happy that we were interested.
I've rattled on a bit but there are just so many great places and experience. Just in parting, Fukuoka and Kyushu in general is a different type of experience. In case you haven't picked up on it, I want to go back again!