If you come by car, it's a lot easier to park outside the historic part. There are a few spaces available, I guess about ten or so, but they are usually taken. And driving in the old part is difficult, this is a very old town , with very narrow streets and they aren't even one-way-streets. Park outside and walk, everything is close together - the whole town is very small!
Ladenburg is on the train line between Heidelberg/Mannheim and Frankfurt, so local trains stop there. The station is about 500 meters walk from the old part. Unfortunately the station is built on a kind of dam, which makes it necessary to climb up or down some steep stairs.
This is really hard to manage if you bring a stroller or have problems walking. There is also nobody around to help, since it is an unmanned train station.
Ladenburg can be reached by train, local trains (RB) on the route from Heidelberg and Mannheim to Frankfurt via Darmstadt stop here. The train ride from Heidelberg takes about 15 minutes. The station is unmanned, the former station building has been sold and is not used by the railway any more.
In the daytime there is no safety problem but I am not sure how pleasant this station will be late at night.
The map (photo 3) marks the location of the train station - this map is put up at the station exit. The old town can be reached in a few minutes' walk. The most impressive approach will be along Jahrstraße, the street opposite the station exit: You walk straight towards Hexenturm and then enter the old town through Martinstor, the only preserved medieval gate tower.