All trains to Stuttgart lead to the Hauptbahnhof Stuttgart on the Arnulf-Klett-Platz. The main train station marks the east end of the shopping area Königstraße in the city center.
All trains and other public transport is available here.

Hauptbahnhof Stuttgart
Arnulf-Klett-Platz
70173 Stuttgart 
From here to the NeckarPark is about 3 km. 

S-Bahnhof Bad Cannstatt
Bahnhofstraße 30
70372 Stuttgart 
From here to the NeckarPark is about 1 km.