I mean Innsbruck is a good start, it's nice city and mostly done with the whole thing in a day.
Goldenes Dachl, the old town and if you take the J line to the hungerburg you have a great view over the City (and you don't have to pay for the Hungerburgbahn).
But as the others say, Salzburg is probably a great for 1 night, Linz is also nice.
Have fun :)