Otsu does not have its own airport. The nearest airport is Osaka's Itami Airport, but Kansai International Airport is an equally viable option. There are no shuttles or limosine buses from either airport to Otsu however, From Itami Airport you can take a limosine bus to Kyoto (¥1,280) or Osaka (¥490) and then continue to Otsu by train. From either airport, you can travel from the airport to Otsu by train.
From Kyoto, take the JR Biwako Line from Kyoto Station to Otsu. Alternatively, you can take the Keihan Keishin Line to Hamaotsu Station. From Kyoto Station, the JR line will be most convenient, but from Eastern Kyoto or the subway Tozai Line, Keihan railway is the better option. (Sanjo-keihan to hamaotsu subway 410y / ~25min)
Subway and JR station are distant of about 15min walk. Walk to Otsu SA is ~25min from JR station if you want hitchhike out.
Gichu-ji Temple (義仲寺). The burial place of famed haiku poet Matsuo Basho, of Narrow Road to the Deep North fame. The temple is 300m away from JR Zeze Station (膳所駅), one stop from Otsu on the JR Tokaido Line. Entrance is ¥200.edit
Ishiyama-dera, (On the Keihan Line, go to Ishiyama-dera Station. Upon exiting, go right for about 15 minutes), . This temple was founded in 749 and the hondo (main hall) is the oldest building in Shiga Prefecture built 850 years ago. Inside the hondo, in the room on the right, is the "Genji Room" where it is believed Murasaki Shikibu wrote her famous book "Tale of Genji", considered to be the world's first novel. The temple precints are quite large, with a 750 year old pagoda and Muyu-en Garden among other things. The pathway leading to the temple is lined with cherry trees, making it especially beautiful in the spring and autumn. For those traveling on the Saigoku 33 Kannon Temple Pilgrimage, Ishiyama-dera is number 13.Entrance is ¥500. edit