If you are interested in old towns, than INN is your choice. Also the mountains around INN are outstanding.
True, Innsbruck and Garmisch-Partenkirchen have a very different 'feel'. But I like the older and often overlooked Partenkirchen. To me it has more charm than Innsbruck. It is smaller and more rustic, but has a lot of tradition and history.
I spent several hours in Innsbruck a few months ago, trying to uncover exactly why it is so popular. Never did find out, but even in November there were masses of tourists milling around. I have been there many times; it just doesn't excite me, I suppose.
My first choice is always Salzburg, but I still don't really understand the appeal of Innsbruck. Pretty, but not that much to see.
If I am missing something, do let me know however!!