I too will assume you mean Monkey Park in Inuyama. If you want to go from Tokyo to Inuyama, then all the way back to Narita city, then yes a JR pass will save you a significant amount of money.
All the locations you've specified essentially radiate outward from Tokyo. I doubt very much that you'll be able to visit all of them without bouncing through Tokyo a few times.
To get to Takaragawa:
Welcome to Takaragawa Hot Spa Osenkaku (click "Access")
Getting to the Monkey Park:
About Us
To Shirakawa-go:
The World Heritage Shirakawa-go
To Narita City:
Narita Travel Guide
Check train routes and timetables here:
Japanese Train Route Finder By Jorudan Co.,Ltd.