I'm assuming that you mean places to eat, and not just "things to do"?
I've been to all of those places, and you should have a good time in each of them. As far as food goes, Vienna has a fantastic market. It is enormous and has tons of great produce, cheese, fish, meat, etc... And definitely go to the original Julius Meinl in the city center - it's awesome.
Munich also has an excellent market, with great places to get a sandwich and a beer as well. Good produce and such there, too. You must get pretzels while in Munich - they are the best that I've had anywhere. And also beer - how could I forget that? They also have great ice cream. There's a great place right on the main platz that's always crowded ( and has really good eis ).
Food-wise, all I remember about Rothenburg was that I ate at a good Chinese restaurant ( really ). In Salzburg, I only recall eating in the apartment that I stayed in.
Austria has some of my favorite wine in the world. If you've never had any Austrian wine before, you MUST try it. The Gruner Veltliners are of course wonderful, but the reds really stand out to me. Definitely try a St. Laurent - it's a great red ( Umathum and Gesselman are great ones ). Also try a Zweigelt and a Blaufrankish - both types are really good. Germany makes some awesome whites, too, but wine isn't as prevalent in Munich as it is in the Mosel/Rhine region.
You should enjoy the trip. I love Munich and have been there several times, There's lots of outdoor things to do - ride a bike ( or take a bike tour ) if you are able. It's a great walk-able/hike-able city. I love Vienna also, and it's also highly walk-able. Salzburg is very nice, and Rothenburg is quaint, but IMO it's not worth much more than a day, as you can see really everything in one day.
Have fun!
Jan