Itinerary Help! (Munich-Salzburg-Würzburg-FRA airport)

Hi Everyone, First time travelling to Germany this summer! I'm very excited but need some feedback on my itinerary. I'll arrive in FRA on Fri, June 27th at 10am and depart from FRA on Thurs, July 4th at 2pm. Over the weekend I will be visiting a friend in Munich. I'd like to fit in some day trips and overnights in other towns. I get stuck planning the end of my trip when I start heading back to Frankfurt to catch my afternoon flight. Here's what I have so far. Any suggestions would be greatly appreciated! 6/28- Land in FRA, hop on train (Bayern-ticket?) for day trip to Rothenburg ob der tauber, train to Munich in the evening 6/29-6/30- Munich sightseeing 7/01- Neuschwanstein & Linderhof Royal Castle and Oberammergau Tour from Munich (Grayline); Overnight in Munich 7/02- Travel to Salzburg, explore, and stay overnight 7/03- Salzburg to Würzburg. (Is there time to visit another town en route?) Overnight in Würzburg 7/04- Direct train from Würzburg to FRA

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