The University of Bayreuth's botanical garden, south of the city centre, covers 16 hectares and focuses specifically on plant ecology — organised not by taxonomy but by habitat type. Sections represent the major ecosystems of the world: tropical rainforest, Mediterranean scrub, alpine meadow, Central European deciduous woodland. It's a different approach from most botanical gardens, and more intellectually interesting.
The garden is open to the public and free to enter, making it a good option for an afternoon walk if you want to get out of the old town. The tropical greenhouse has an impressive collection of carnivorous plants and orchids. The walk from the city centre takes about 30 minutes; alternatively, the university bus route connects the town to the campus.