Bycicle tour around Lake Biwa ! Can be done in one or two days. There is a great volunteer organisation for international communication and exchange (VOICE) in Hikone that takes care of this once or twice every year and they have a lot of other tips too! Very nice people!
Fantastic site-seeing of Lake Biwa. Great accomodation at bungallows on the beach in Omi-Maiko town. BBQ at sunset, and sun rising from the water in the morning (if you wake up!!)
this is not exactly in Otsu, but is 40 min by JR train towards Maibara. Actually it is another city -called Hikone (unfortunately no listing!). The Hikone Castle is a 'must see' in spring (sakura blossom) or autumn (momiji leafs).
take a boat from Otsu to visit the Biwako Museum (the lake museum), and surrounding park. (or U can get there by bycicle, on the lake side road, about 40 min.)
Fondest memory: Kite flying near Biwako...