The main street of the Old Town (Altstadt) historic district is Herzog-Friedrich-Strasse, which becomes Maria-Theresien-Strasse, the main axis of the postmedieval New Town. Altstadt developed on the right bank of the River Inn, site of the baroque and medieval buildings that give the city its architectural flair. To the south, Altstadt's boundaries end at Burggraben and Marktgrabben. After 10:30am, it becomes strictly pedestrian, but that's all right, since the best way to see that part of Innsbruck is on foot.
Most of your explorations will be in Altstadt, because (with a few exceptions) the New Town contains mostly residential neighborhoods. The dividing line between the Old and New Towns is Egger Lienz Strasse.
The Inn River divides this historic city into left- and right-bank districts, and many of the attractions, including the Hofkirche and the Goldenes Dachl, are on the right bank (in Altstadt). There are two major crossing points over the river; the Universitätssbrücke and the Alte Innsbrücke (Old Inn Bridge).
If you arrive at the Hauptbahnhof (the main railway station), take Salurner Strasse and Brixener Strasse to Maria-Theresien-Strasse, which will take you into the very heart of Innsbruck.