You would do best to fly open jaw into Munich, and out of another city--Prague or Vienna.
You might want to look on Mapquest or GoogleMaps.com to get a lay of the land. The distances you'd be traveling are much farther than you realize. Your planned itinerary is just not do-able in the time allowed.
Bacharach is just a small village beside the Rhine River with some castles in the area. It's not but a few hundred yards long. On my two trips, Bacharach was more a place to spend the night than a destination. I also find the Black Forest okay, but it is another region to drive through.
One thing you didn't say is if you've ever been to Germany and/or Europe. 10 days is pretty short, as Munich is a great city that deserves 4 days to see the many local sights and soak in the Bavarian culture.
You could drive southwest of Munich to Fussen and end up in Innsbruck for the night. The mountain scenery in this drive is incredible, and it's really not that far. You could drive up to Munich area and turn the car in. Then take a train over to Salzburg for 2 nights.
Take a train to Prague or Vienna for the balance of your time. Either is a great European city worthy of 4 nights to see the sights.
And if at all possible, try to stretch your trip another few days.
To take on more cities might be counterproductive. Vienna is actually a better city to fly to the U.S. from than Prague.