Just a nice walk
Otsu itself is not a great tourist destination. However, it's very close to Kyoto (about 20 minutes by train), which has hundreds of places of interest.
If you're feeling a bit overwhelmed by the Kyoto temples and museums, you might want to hop into the train and head for Otsu. This city is right in front of Lake Biwa, and you'd probably enjoy walking along the sidewalk that stretches along the shore.
For lunch, you could just buy some boxed lunch at 7-Eleven and eat sitting on the grass or one of the benches facing the lake. Or you could eat at one of the two shopping centers near Keihan Hamaotsu station.
There's also a boat restaurant that leaves from the pier near Keihan Hamaotsu station, but I've never tried it. I didn't feel attracted because they try to give the imression it's an American boat, complete with caucasian entertainers. I think they call it the Mississippi.
Nothing wrong with white people. But if you go sightseeing in Japan, I think the last thing you want to see is a Deep South inspired show.