For a nice hike near Basel, Switzerland, only a short tram ride, you’ll find the path to the Castle Landskron. At the end of the Tran 11 (direction Flüh) you’ll find the path (Wanderweg) leading you towards Landskron. The trail follows the Solothurner Wanderweg, but will lead you into France and to the Castle.
The Castle sits in Leymen, France, with the path zig-zaging the boarder. The beginning is mainly uphill, but the reward is a rather large castle with commanding views of the area. This makes for an easy morning or afternoon activity and brings you to one of the largest ruins in the area.
For more information on the Castle Landskron, route and directions to get there, here are some helpful resources.