Are both of these sentences correct? Does the position of the prepositional phrase matter here?
What do you want to talk with me about?
What do you want to talk about with me?
OP's two different word sequences are both valid, and it's not really worth exploring whether there could be any nuance of difference between the meanings, but to talk with [someone] is somewhat more "poetic, formal, dated" than the more common talk to someone. That makes OP's first version look slightly "starchy" compared to the second.
But it's equally valid (and much preferred) to use that alternative preposition in OP's example...
There are no hits at all for either of OP's exact examples in Google Books (which optimistically estimates "About 8,370 results" for my alternative, though there are actually only a few dozen if you scroll through).
That difference in "prevalence" probably isn't as significant as those results might suggest though. Most native speakers in most contexts simply wouldn't be likely to notice anything remotely "odd" about the versions that don't turn up in Google Books. I'm going out of my way to make a fine distinction.
EDIT: I though it might be interesting to see how talk to has edged out talk with over time...
1) Q: What do you want to talk with me about?
The declarative would be: I want to talk with you about the job.
That's fine. I would say it's somewhat more spoken than the other one.
2) Q: What do you want to talk about with me?
The declarative here would be: I want to talk about the job with you.
The actual order of the words is: talk about something with someone.
To talk with someone about something is not the natural order. But it isn't wrong per se.
Since the verb is to talk about something with someone, I see no reason for putting the about at the end. To me, frankly, it is just less elegant in terms of the actual order of the declarative form, which is the basis for questions, if one is being picky.
When there is no with or to, for that matter, the declarative and interrogative are:
I want to talk about the job. Question: What do you want to talk about?
So, for me: What do you want to talk about with me? is more natural. With plus a pronoun gets added on there. That's why I prefer sentence 2.