This little-known place, 1km before Asklepieion, does not have the immediate 'wow' factor due to its modest collection. But it should. It houses a small text-heavy exhibition on Hippocrates, explaining the oath for doctors, plus ancient medical instruments, the likes of which are still used today. The highlight is the botanic garden, growing herbs and plants that were used in Hippocratic times.
Note: it is not a pruned and sculpted garden and this is intentional. Its 'scrappy' nature is authentic and the plants are grown in the conditions they would have been in ancient times. Given there's no video information at the Asklepieion, this provides wonderful context to the workings of the healing centre.