I just returned from a visit to Nagoya. As you mentioned, all of the hotels within Nagoya were sold out. I ended up staying at the new Comfort Hotel at Central Japan International Airport for US$83 per night. It's about a 28 minute train ride to Nagoya Station from the Airport railway station (850 yen for the express train - 37 minutes, an additional 350 yen for the rapid express train with all reserved seats - 28 minutes.) The hotel was a three minute walk to the airport / train station. The rooms were small (by U.S. hotel standards but not European standards), but all the furnishings were new, the room was exceptionally clean, and the staff were exceptionally friendly and helpful. Although not the ideal place to stay when visiting Nagoya, due only to location, it is a good option when hotels are sold out in the city.

You might also try the Japan Travel Bureau. I contacted an agent at the San Francisco office and she was quite helpful. She actually found me a room in Nagoya for about US$115 per night but I took too long to get back to her and subsequently lost the reservation.

Have a great time in Nagoya!