After reenlisting, how do I go about choosing my next duty station?

Well I think that dog has run, now. You should have made it a condition of your re-enlistment. Now, I suspect you'll get The Needs of The Army.

I'm assuming you haven't reenlisted yet. You'll talk with your Career Counselor, pick a duty station, and then reenlist. The duty location will be listed in your contract.

Call your branch manager you can find his information in the HRC website.