Munich airport to Innsbruck

Lufthansa has buses from the airport to Innsbruck. Otherwise, take the train, which will require a change at München Hbf.

Take a look at the route that takes you around Munich using A92, A99 and A96 to A95 towards Garmisch-Partenkirchen. From just before Garmish it is secondary roads. No need for the Austrian Vignette as you can skip that 10k stretch of A12 into Innsbruck. The road is a steep downhill from Seefeld to Martinsbühel, AT, but nothing to worry about. The trip is 2.5-3 hours, but if you want to stop Garmisch-Partenkirchen might be the place. Halfway might be off A95 somewhere on the east side of the Starnberg See (make reservations). With a Navi I would set it to "No Tolls." Be wary of speed cameras along the route in Austria.

Then the toll itself is between $25.00 and $30.00.

Correct me if I am wrong, but I believe the toll is to use the Brenner Pass, which is not between Munich and Innsbruck. Its between Innsbruck and Italy.

first a vignette (tollway pass) apparently must be purchased for about $10. Then the toll itself is between $25.00 and $30.00

The $10 is for the Austrian 10-day vignette, which is required on the highway from the Austrian border. It's available at filling stations between Munich and the Austrain border (Holzkirchen, Irschenberg, Brannenburg). Beyond the vignette, there are no other tolls. You may have seen a reference to the Brenner toll (i.e., for the highway from Innsbruck toward Italy).

I recently tried to but the Austrian Vignette online. You need to do it 18 days in advance. I buy mine at ADAC in Germany. You can get the digital one the same day there (no sticker). There are a few stretches of the Austrian Autobahn that do not require a Vignette. There are also stretches that have an additional toll.
https://www.asfinag.at/en/toll/vignette/

We are going to be tired from the Chicago flight

then is getting in a rental car and driving on busy roads (the A road can get very busy) in a strange country the best idea?

A train from inside the airport to Munich main station (Hbf) is fast and frequent, and then it is an easy to get the scenic train which goes from there to Innsbruck. It really is that easy.

I agree with Sam. We’ve driven from Munich airport to Innsbruck and Innsbruck to Munich airport a number of times and never encountered a toll road. Vignette is only 10€ for a 10 day toll sticker.

What roads did you see have tolls of $25 to $30? I’ve never encountered these on our trips.

As an option, you could train to Garmisch, stay or base there and pick up a rental car there. Mittenwald close by is also an excellent place to base.

Paul

take the train, which will require a change at München Hbf.

You probably want to make the change at the Ost Bahnhof. The ECs, which go through Innsbruck on their way to Italy, stop at München Ost. Or you might take a regional train, change at Rosenheim and switch to an Austrian local train in Kufstein. The regional train to Rosenheim will also stop at Ost.