"Meet the First Drop of Lake Biwa! Water-Source Discovery Trekking" has become such a famous trekking expedition, it has even set up collaborations with big outdoor gear manufacturers. There's also a full range of other outgoing trekking courses, including the Kojorogaike Course that lets you look out over the beauty of Lake Biwa while heading to an ancient pond with 6,000 years of history and legends, and the Hiradake Course that takes you through some glorious forest valleys while bird calls soothe your senses.
If you're looking to take a stroll that's a little more relaxed, the course around Biwako Valley itself comes highly recommended. If you start to feel tired you can even take a rest in a forest hammock.