Getting around

Trams, tickets, cycling and trains out of town.

Short answers

Trams and the KVV: The KVV network runs trams through the tunnel under Kaiserstraße and tram-trains out to the Black Forest and the Palatinate. The Deutschlandticket covers all of it.
Cycling: Karlsruhe regularly tops the ADFC bike-climate ranking for large German cities. A used bike and a good lock are the best first purchase you'll make.
Trains out of town: The Hauptbahnhof has direct high-speed links toward Frankfurt, Stuttgart, Basel and Paris. Strasbourg is close enough for a day trip.