The city is not very big so you can walk everything within less then 30min.
Parking your car in the city is cheap. Usually you pay €1.00/hour but there are numerous parking lots for 5 to 10 Cents/30min. Click the link for detailed info on parking zones in town:
Access by car is via the A6 Autobahn (Heidelberg-Nuremberg) and the A81 (Würzburg-Stuttgart).
Heilbronn lies on the major Stuttgart-Würzburg rail line with frequent service.
Heilbronn is situated on the Neckar which flows into the Rhein River. There are several shipping companies offering tours along those rivers.