The official fare from Noi Bai Airport to Old Quarter is USD15. You agree on the fare before you board, however the driver may or may not agree with a "stopover" at the USD15 fare.

I would suggest you either negotiate with them (they will definitely ask for a higher fare); or pay the USD15 to get to the travel agent (which I am assuming is located in the Old Quarter) and then get the travel agent to call for you a meter cab to get to the train station.