Munich, Bavaria, Salzburg itinery

I'm not sure what you mean by "the Bavaria area". Bavaria contains Munich and it's the largest federal state in Germany. Which part of Bavaria did you have in mind?

Garmisch-Partenkirchen is one of the most beautiful places on earth. I would definately recommend staying there. It's a little less convenient to Neuschwanstein, but you can easily take a day trip there. For Zugspitze, it's the ideal location. The ascent isn't worth your time in rainy or cloudy weather. From GaP, you can easily judge from yourself if conditions are favorable, whereas if you stay elsewhere, you can't make the this assessment until you've already arrived in town.

Your destinations are all close together and train travel from Paris will be through Munich, even if you make additional connections on your arrival day. If you will fly out from Munich, then save that city sightseeing for last, to avoid multiple hotel stays in the same city. Otherwise, the order of visiting will not make much difference. Discounted Paris-Munich train tickets are for sale now for all of September travel on the DB train site.

I can't thank you both enough for the helpful information you took the time to share!

Bavaria is huge and there is lots to see but it sounds like you are talking specifically about the alpine area south of Munich and maybe Berchtesgaden. With so little time, I'd base myself in Munich and Garmisch Partenkirchen (there are other good bases but you seem to really like the idea of Garmisch). Neuschwanstein can be done as a day trip from Munich by public transportation, I've never done it from Garmisch so can't speak to that as an option. Personally, I'd try to make it a priority to visit Linderhof Castle, if you can. I find it a more interesting and slightly less touristic experience than Neuschwanstein.

Visit Salzburg as a day trip from Munich and skip Berchtesgaden for this trip, it would take up too much time, but ... if you have your heart set on it, then spend two nights in Salzburg and see Berchtesgaden as a day trip from there. It would take too long as a day trip from Munich.

Hope you find this helpful.

Visit the Partnach gorge in Garmisch if you get the chance

Thanks for the tip, I will check it out for sure!