Tokyo to Nagoya daytrip for castle and...?

Have a trip to Japan in a few months, and we are taking the Shinkansen from Tokyo (staying in Shibuya district) to Kyoto half way through. That's not a problem.

I want to stop at Nagoya for the day before getting to Kyoto for the rest of our trip. Mainly I want to see Nagoya Castle. Looking for some tips, tricks and sights to see.

We are OK leaving Tokyo early, getting to Nagoya, but want to get to Kyoto before it's too late in the day (like by 6:00PM at the latest). So what can be done (and recommended) in about 6-8 hours in Nagoya? How's the science museum, Atsuta-jingu shrine, etc.?