I would agree with the information provided so far about staying at one of the two hotels mentioned right by the airport. I've been to Centrair countless times both as a passenger and when picking up/dropping off someone. It's one of my favorite airports! BabyTokyoKid (who'll be 2 next week) loves going out on the observation deck to watch the aircraft taking off and landing. There's a lot to do/explore throughout the entire terminal. Oh! And it's quite child friendly, too. You can use a free baby stroller since you're flying. Just ask for one at the information desk located in the center of the departure check-in counter floor. There are nice, clean infant changing/feeding rooms at either end of the same floor as the check-in counters, in the middle near an elevator and the escalators, as well as by the gates after clearing immigration.

If your flight arrives around mid-day, you might want to consider staying at the Marriot Hotel over Nagoya Station. From the airport to Nagoya Station it's an easy 25 minute commute by train. Upon exiting the train at the airport there are many free luggage carts available. In and around Nagoya Station there are many restaurants. Across the street from the station and the Marriot you can easily find all sorts of restaurants in the Midland Square building, as well as in a buidling by the Matsuzakaya Department store. Just ask at the hotel. Also, from Nagoya Station, you can take a five minute subway ride on the Higashiyama Line to Sakae where there are all sorts of restaurants and shopping. If you want to by some books on Japan, visit Maruzen bookstore.

If you need any further information, I'd be happy to help you. Having lived in Nagoya now for about 5 years (I'm originally from the Boston area) I'm quite familiar with Centrair, Nagoya Station, Sakae, and other areas in case you're interested in doing some sightseeing (Yes. There are some worthwhile sights to see here in Nagoya). If you opt to stay around the Nagoya Station area, depending on the day, I'd be glad to meet you somewhere and show you a nice, historic area about a 10 minute walk away. Most foreign tourists don't know about this historic area.