Milan to Innsbruck via?

You might want to check GoogleMaps on any such trip. The Alps gets in the way from Milan to my beloved Innsbruck.
It's 4 hr. 48 minutes and 398 km (245 miles) going east to Verona and north on the controlled access highway thru the Brenner Pass to Innsbruck. Going north thru Lake Como area is a more difficult drive and somewhat farther.

Bolzano and the Iceman museum makes a great stop, even if you don't have time for an overnight; museum closed most Mondays. Open-air produce market open every day except Sundays.

There are three itineraries from Milan to Innsbruck:

1. the easy one through Verona and the Brenner highway
   Both the Italian and Austrian highways are toll highways. The Austrian sticker is not needed if you exit at Innsbruck Süd, but if you go on the sticker is required

2. a longer one, Bellinzona, St. Bernardino pass, Chur, Liechtenstein, Feldkirch, Arlberg tunnel
   Both Swiss and Austrian highway stickers required, extra toll for the Arlberg tunnel. This itinerary is easy and scenic, somewhat longer than the Brenner but less traffic

3. via Lecco, Chiavenna, St.Moritz and following all the Inn valley - nominally the shortest, but very long to drive and tiring

I have driven something like fifteen times both itinerary #1 and #2, I prefer #1 as being really quicker, but in days of intense traffic (i.e. all the late July and August weekends) in which case #2 is really better. I drove #3 once and I am glad I did, not really looking forward to do it again.

A fourth itinerary could be Lake Como, Chiavenna and the Splugen pass, then Chur and like #2, but the Splugen pass looks like a lot of curves. Probably only Stelvio pass is as curvy.