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 ;-)