The Toyota Automobile Museum is a fantastic place to be for any car enthusiast. The collection includes a wide variety of foreign and domestic classics.
The experience begins before even reaching the museum; the location of the museum is on a magnetic train line, which seems very futuristic (and has an incredibly smooth ride!).
One of the highlights from the museum is the Toyota 2000 GT, which was featured in the James Bond film, "You Only Live Twice". In the movie, it is shown as a convertible because Sean Connery wouldn't fit in the original car!
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Getting to the museum is fairly easy once you make it to Nagoya station. Take the Higashiyama Subway and get off at Fujigaoka, then transfer to the Linimo line (a Maglev train!). Once on the Linimo, get off at Geidai-dori. The museum is huge and impossible to miss, so there should be no problems after that. There are more details on their English website:
http://www.toyota.co.jp/Museum/english/
Hope that helps!
In May, there is a national gathering of classic car owners near the museum in Moricoro park. This year it will be May 26th.
There is also a museum in Toyota that goes into the history of the company. Both have beautiful cars to drool over.