Short version: city = Yuzhno-Sakhalinsk; island = Sakhalin
Slightly longer version: People often refer to this place as simply "Sakhalin" and while that's sort of correct, that's not actually the name of the city. I'm in Yuzhno-Sakhalinsk, the largest city on the island of Sakhalin. The island is part of Russia's Far Eastern Federal District, though that was not always the case. It is worht noting that the Far Eastern Federal District is not part of Siberia. It's even further east as the http://en.wikipedia.org/wiki/Siberian_Federal_District>Siberian Federal District is to the west of this region. So yes, there is a place past Siberia, though it really depends on what direction you're travelling.
Why are we all here? For the eminently originally named Sakhalin-I and Sakhalin II projects. What can I say, people like functional names. Though apparently all the fields in the Sakhalin-I project are named after birds. Probably tasty birds.