Which part can I visit together with Nagoya?

I am going to Nagoya in Mar 2020 for 7 days. Which part of Japan can I visit together with Nagoya for my 7 days?

Lots of places you can add on.
One of the closest is Inuyama - the quaint castle is one of the 12 surviving originals (not reconstructed) and the nearby Meiji Mura is the finest open air museum in the country.
https://youtu.be/ZgYDE7ujk8A

You can go see the Kiso Valley in Nagano.
Or go visit Takayama and Shirakawago.
Go to see Ise Shrine.
There is Gero hot springs north of the city.
Not to mention Gujo Hachiman.
Hikone to the west has some very good sights, especially its castle.
https://goo.gl/FRe6t8
Matsumoto is about 2 hours away; pushing it but doable.
There is also Iga-Ueno is Mie.
Otsu has its share of sights as well.
And actually, Kyoto is just 35 minutes away by bullet train.

How much for the bullet train from Nagoya to Kyoto?
Do I need to stay 1 or 2 days at Kyoto or Osaka?

You can check rail fares, schedules and transfer info on Hyperdia.
http://www.hyperdia.com
An adult unreserved seat appears to be going for 5070 yen. It is close enough for a day trip time-wise, but I suggest you stay there for a few nights (the more the better).
https://goo.gl/knQtMg
You could spend months in Kyoto and not see it all. But you can get a good taste of the place, and you could also spend your evenings in Osaka, which has a great night life.
http://goo.gl/XE5R94

Following sites are off the main touristic path and quite enjoyable:
* Site of Reversible Destiny
* Nagashima Spa Land
* Inuyama (castle)
* Gifu (castle / Comoran fishing)
* Mino (espeically if you have interest in paper)
* Gujo Hachiman