You can even see the Leuchtenburg Castle from Jena's heights, because it is located somewhat south of the city on the top of a hill.
The castle has belonged to the private Leuchtenburg Foundation since 2007, which is why admission is also relatively expensive.
Although it is an old castle, it has been very well renovated and today contains a museum about porcelain (Porzellanwelten) and one about the castle's history. A lookout tower can be climbed for a view into the distance.
If you don't want to pay anything, you can simply walk around the castle on the panorama path.
There is a beautiful but a but challenging hikinh way from the city Kahla to the castle while having many viewing points.