Which is correct?
The price we quoted for you
The price we quoted to you
I often stumble with this. I'm not sure how to use for you and to you.
While I think they mean roughly the same thing, I do see one difference between those two.
As Edwin suggests in the comment above, The price we quoted to you is exactly identical in meaning to The price we quoted you
Maybe I disagree with Edwin (or maybe not), but I see a small potential difference in the for you construction. The price we quoted for you means The price we quoted for your sake.
With ditransitive verbs, we usually think of the preposition-less form as implying one particular relation between that object and the verb. For quote, we assume "to". If you say for you, then you mean
Thus, to give a similar example:
The poem I wrote for you
= the poem was something I wrote on your behalf
The poem I wrote to you
= The poem I wrote to give to you
The sentence the poem I wrote you is identical in meaning with the latter.
To give a dissimilar example, the cake I baked you is identical to the cake I baked for you and the cake I baked to you is ungrammatical.
'For' and 'To' have many different uses in different situation.
In your case above this would be the correct answer in my opinion:
The price we quoted to you.