If "seeing a couple of wineries" means wine tasting, driving is not the most sensible choice. Even less so with jet lag. By train your trip will be much more relaxing.

Local trains run along both river banks and stop in every town and village. You can easily take a train to, say, Bingen or Bacharach, board a boat there downstream and one way to St. Goar or Boppard and hop on a train back from there.

But if I take the train to Bacharach for instance, how would I be able to go to any of the wineries/castles? I'd imagine these are not walking distance from the train station?

Bacharach is small and walkable. There will be more than enough wineries and wine shops in the town center. Castle Stahleck is on a hill right above the town.

Same with St. Goar and the ruin of castle Rheinfels.

Or Oberwesel, another worthwhile stop along the train route.

This website is a goldmine of information about all the places in the Rhine gorge: www.welterbe-mittelrheintal.de/index.php…

Middle Rhine Valley =

hills (often with a castle) + railroad + road + Rhine + road + railroad + hills

And at the few places where there is more space there is a small town. Built long ago before cars existed. With this setup parking is of course a problem.

Best pace to explore the Middle Rhine and best views are with the boats. That's why they are rather popular and frequent there.

By train or car the views are more one sided. And with their speeds you have already to know exactly where exactly to look at, otherwise the castle is already out of sight after a couple of seconds. And if you drive by your own you cannot look around anyway. The driver has to concentrate on the road/traffic in Germany. Not on the landscape. Otherwise this will end badly. You can also not stop just anywhere, only at designated parking spaces.

Another thing to consider are potential road traffic problems towards Frankfurt Airport. Frankfurt (with Mainz etc.) is one of Germany's biggest conurbation. Inclusive the usual traffic problems (traffic jams etc.).