What is the correct placement of the word "exactly" in a sentence and why?

Example :

1. I want to study in another country, but I don’t know exactly where.
   vs
2. I want to study in another country, but I don’t know where exactly.

For me, both are correct, as both imply that I don’t know the exact place I will go to study. If anything, I prefer no. 1 as I think sentence no 2. needs a comma after the word "where", as if the word "exactly" has been added as an afterthought.
Can anyone enlighten me?