A recent question asked about the impropriety of "Where's it at?" The question started me thinking about when at is allowed with where. My first thought was that ne'er the two should meet: at is always extraneous.
Some verbs, though, seem to give more room for the pairing. "Look at where" or "point at where" are far less strident than "sit at where" or "is at where". Still, "look where" and "point where" are far cleaner.
It seems to me that at is more permissible when the subject is not at the location stipulated by where. In the two examples above, the subject is one place and directs her attention "at where". The at becomes a way of keeping distance between the subject and the place.
What is the function of at when it precedes where?
Best Answer
Yes,
could be valid, because in that construction, "where you want to go" is a noun phrase, forming the object of the preposition "at".
Similarly
the same phrase also acts as a noun phrase, but here it's a predicate nominative.
And
Where I want to go is none of your business!
the same wording also acts as a noun phrase, but here it's the subject of the sentence.
So your suggested "at where" is a normal (preposition) + (noun), like "at the beach".
Disclaimer: nothing in the above should be construed as sanctioning the "where are you at" construction, which is another matter entirely.