Bonn is compact enough that walking covers most of the centre, but the city's tram and bus network makes it easy to reach Bad Godesberg, Beuel, and the Museumsmeile without a car.
The Stadtbahn (light rail) and bus network is run by SWB and integrated into the VRS regional system. A day ticket covers unlimited travel and is good value if you plan more than two trips. Tram 16 runs the main north-south axis from the Hauptbahnhof through to Bad Godesberg.
Cycling is popular and practical -- the streets are manageable, bike lanes are common, and rental bikes are available around the station. The Rhine promenade makes for a pleasant ride.
Taxis are available but expensive by German standards. Rental cars are useful mainly for day trips to the Eifel or the Ahr valley; within Bonn itself, public transport and walking are the better options.