The Botanischer Garten attached to Friedrich Schiller University is one of the oldest university botanical gardens in Germany, dating from 1586. It covers 4.5 hectares in the middle of the city, a few minutes' walk from the university main building and directly beside the Zeiss Planetarium.
The garden is well maintained and genuinely interesting as a scientific collection, with a good tropical greenhouse, a rock garden of alpine plants, and a historical section tracing the formal garden layouts of earlier centuries. It is also simply a pleasant place to sit in a city that is otherwise quite urban in its feel. Free to enter.