the major attractions in Innsbruck are near each other such as the golden roof, hofburg palace, town square, sankt jakob church, maria Teresa strasse, hofkirche, leopold's monument, stadtmusuem, etc and such, walking is the best way to go around Innsbruck as the city is small and compact and the streets, even though many are cobblestones, are relatively flat and there are no inclines. most tours of innbruck are walking tours as the big tour buses could not enter the streets are they are small but not crowded at all.
The train station is very close to the main centre of the town and makes travelling easier to other cities such as Vienna & Salzburg.
Travelling by trains...trams and walking is the best moe of transportation. However if you plan to visit the Swaroski museum a car is ideal. It takes about an hour to reach there and is a must visit!
Innsbruck has a tram and bus system which is quite good and it has quite a few stations as well. But still it's small enough to walk almost everywhere! Or then again, you could also pay lots of money to get a "Fiaker", a horse drawn carriage! (If you ever see me inside one anywhere in the world you can shoot me ;-)