Nagano to Nagoya

What is the best route from Nagano to Nagoya if I want to visit Shirakawago and Takayama,at the same time taking in the sights of the Japan Alps in December.
Tks

Takayama and Shirakawa-go are not located along the way from Nagano to Nagoya.

For cost-effective travel, you could:

Take a bus from Matsumoto to Takayama. Then take a bus from Takayama to Shirakawa-go. You can then travel back to Takayama and onward to Nagoya by train, or travel straight to Nagoya by bus (must reserve seat).

Of course, you could just go by train to Nagoya and then by train to Takayama. Shirakawa-go can only be reached by bus. This will be the most cost-effective if you have the JR Pass but will probably be the most expensive without it.

By trains or bus usual.

Self drive not recommend if snow driving experience not enough.

I'm with Rabbityama, and I'd stop at Kamikouchi between Matsumoto and Takayama.

But as an alternative you can go by train from Nagano to Kanazawa (change at Naoetsu), total time about 3 1/2 hours, then check out Kanazawa, bus to Shirakawa then bus to Takayama, then train to Nagoya. That'd be a nice trip with no doubling back.

Personally, I'd do that trip with overnight stops at Kanazawa and Takayama. But I call myself "Lazy" for a reason.