+1 Sigurd, make sure that your rental car allows travel to all the counties you want to visit.
www.sixt.com may be able to help - they are the Hertz of Europe.
I lived in Munich for about 3 years. It's a beautiful city about 30 min. fro the foot of the Alps. You can visit Schloss Neuschweinstein "fairy tale castle" easily from there on the way to Innsbruck. There is an "alpinestrasse' above GArmish-partinkierschen that is amazing. Go to Vienna and Venice (you'll have to park your car to go to Venice, unless you get one of these -
HTTP://www.time.com/time/2003/inventions/invaquada.html
Drivers in different countries drive differently...although the rules of the road are basically the same. German autobahn has no speed limit where indicated. Driving fast in Germany is a must.
Italian drivers drive smaller care and weave in and out of traffic like aggro NY drivers.
Don't get me started on the French...
For a driving vacation, I'd spend a lot of time in Germany. Go the the Porsche factory in Stuttgart, drive the romantic road, go to the BMW museum (and factory tour) in Munich, Check out Berlin, perhaps drive through the black forest to Prague, then to Slovakia, into Austria to Vienna then on to Zurich...I'm jealous, I miss Europe.
note - "right of way" is literal. At an intersection of ANY kind (small side street entering arterial road) the vehicle coming from the right has right of way. This includes bicycles. There is NO "right on red" unless explicity stated.
Best of luck - have a GREAT time.