Lake Victoria is the largest lake in Africa, measuring almost 70,000 square km — roughly the size of Ireland. The Kenyan shore, centred on the city of Kisumu, is Luo country, and the lake has shaped the life and economy of the people here for centuries. Fishing remains central, though the industry has been badly affected by the invasion of water hyacinth, an aquatic weed that chokes waterways and robs fish of oxygen. Bilharzia is prevalent in the lake — do not swim in it, and wear shoes on the banks.
The lake itself is not dramatically scenic, but there are several islands worth visiting. Rusinga Island is connected to the mainland by a causeway. From Kisumu, take a matatu to Homa Bay, where you can get transport to the island. There is a mausoleum for Tom Mboya, the Luo political leader assassinated in 1969, but not much else.
If you want to get properly off the beaten track, go to Mfangano Island, reachable by ferry from Homa Bay. There is little on the island except a local community and good fishing. It is one of those places where you arrange to stay with locals and experience a pace of life that the rest of Kenya has mostly left behind.