Zurich islovely but, at least for me, Munich is better. And cheaper.
Personally, I would go to Salzburg, one of my favorite places in Europe. It has an excellent old town with lots of culture and things to see and do there and nearby. As it literally sits on the threshold of the German and Austrian Alps, there is excellent scenery nearby and interesting things to visit such as the unforgettable ice caves by nearby Werfen which also has an excellent medieval castle.
I love train travel in Europe from city center to city center but a train from Innsbruck to Zurich is 8 to 9 hrs if you look on the link above and only about 2 hrs or less to Munich and only 19 euros if you buy and print your non refundable ticket soon on either one of those sites. Plus 0 change of trains to Munich. For eg there is a 10:36 train from Innsbruck arriving Munich at 12:25. That special savings fare ticket can go up to 40 euros if you wait and buy on the day of travel. If you take local or regional trains to Munich those prices are a low price even if bought on the day of travel and may only add an hour of travel with the same beautiful scenery to take photos of from your large train window. If you take the local train from Innsbruck north a little less than an hour to the beautiful and interesting town of Mittenwald and stay a night or 2 there, you could then on your next day of travel buy a low priced Bayern Laender train ticket which allows unlimited train travel until 3 in the morning anywhere in the large German state of Bavaria. The Bayern ticket can be used from 9:00 on weekdays and from anytime on weekends and is good all day on all regional trains in Bavaria (not the high speed ICE trains) and even includes your buses and regional trams in Munich for transportation to your hotel and tourist sites. From Munich you can use the same type of ticket for a day trip from Munich to the famous German castles in the Fuessen area. The bus that meets the Fuessen trains going to Neuschwanstein and Hohenschwangua castles is also included with the Bayern ticket. It also incudes the buses that take you from the castles to the base of the lifts going up the mountain where you can eat and watch the hang gliders and enjoy the gorgeous lake and mountain views. On another day you could use a Bayern ticket from Munich all the way to Salzburg, Austria, maybe even stopping half way to visit Herrenchiemsee Castle on the island in Lake Chiemsee. From Salzburg there is a bus that goes to the beautiful Berchtesgaden area for all those famous sites. In the another direction from Munich you can day trip on a Bayern ticket to Rothenburg, Nuernberg, Bamberg, or Regensburg. On another day you could day trip from Munich on a Bayern ticket in the direction of Ulm or Augsburg. You might also investigate on the links at the top of this post other German rail passes beside the Bayern Laender ticket, looking under "offers". There are probably other even cheaper all day passes for the Munich only area. I was 5 days in Zurich attending a convention in the past and I was traveling in southern Germany a little over a year ago. Both Switzerland and Germany are beautiful but because of all the above reasons and because Germany's hotels, restaurants, and train travel would be so much less expensive I say go to Munich. If you plan to visit a lot of the castles and other tourist sites in Bavaria you should think about saving money buying a Bavaria Castle pass. I know there is a link on the Neuschwanstein Castle web site that takes you to the Bavarian Castle Pass web site and tells the price and what places are included but you can purchase it at your first site. Also if you are doing the Neuschwanstein Castle on a day trip instead of overnighting at the castles (if you overnight take the lovely walk around the lake or the walk going through the lovely fields going toward the mountain lift) you may want to reserve an entrance time on the castle web site since I am guessing it will be crowded with day trippers in June. The site will reserve an entrance time with a credit card but you can use the Bavarian Castles Pass to pay when you pick up your ticket which is by far the shortest ticket line to enter t famous castle. Also on your way from Innsbruck to Munich is the famous Zugspitze. You might find it beneficial to buy a Rick Steve's Germany guidebook or download it from his web site. His books will save loads of time and money with his great city and country maps, hotel and restaurant suggestions, and even details such as the bus numbers and exactly where the bus stop is located. Also download his free and fantastic Munich and Salzburg walking tours if you plan to go there. www.ricksteves.com/news/audio-tours.htm
Munich!! Zurich is lovely but SO expensive it just took all the fun away. There is a lot to see and do in Munich. You won't be disappointed. Munich is very reasonable and easy to get around.
You don't give a date in June when you would be traveling from Munich to Geneve. On June 18 and most days in June there is a train leaving Munich at 7:17 and arriving Geneve at 14:42 (7:25 hours) with only 1 change of train in Zurich and it only costs 39 euros if you buy online and print your ticket soon, but remember most low priced tickets are nonrefundable and nonchangeable. When you buy and print your ticket to Geneve or to Geneve airport on the German rail site you can put a stopover in Zurich for up to 24 hours. reiseauskunft.bahn.de/bin/query2.exe/en…
I haven't been to Zurich, but agree with all the previous posts. Munich is a lovely city, it has a blend of new (art museums, BMW ) and old (Nymphenburg, Hofbrauhaus etc) and close to Fussen where everyone wants to go for the King Ludwig castles. You can do a bus tour that takes you to Neuschwanstein, Hohenschwangau and Linderhof. You are a quick hop to Berchesgarden, Salzburg, Garmish.
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