Gagarin Park
Scrappy but loved, the 220-acre Gagarin Park is a nice place for a stroll, supposedly the largest in the far east and something of a leisure center for the local population. The park features athletic facilities, adventure playgrounds, a lake with small boats, a miniature railroad for kids, a zoo and a run down amusement park. On the eastern corner of the park there is a trail head leading up the hill for a nice view over the city.
Chekhov International Theatre Center
Really not that much "International" about it, this theatre is in a rather unusual for a frontier region building covered by mosaics in the socialist realism style 1964. The theatre has roots back to the 1930s. It sometimes has musicals and concerts on the repertoire, if sitting through 2 hours of incomprehensible Russian is not your thing.
Gorny Vozdukh Ski center
An alpine complex located within Yuzhno-Sakhalinsk city proper. It has nine runs 1 black, 5 reds & 3 greens and three lifts, including a spanking new 2.5 km gondola lift. There is also a bit of English information on the local snowboarding federation's website (http://www.snowboard.kato...).
Sakhalin Diving
This PADI dive shop can help with tours to Moneron island, listed in the Sakhalin guide. There is also a diving club on Kommunistichesky Pr 19 [email protected]/42-26-91
Sakhalin Regional Puppet Theatre
While mostly geared towards children, some of their shows are actually quite extraordinary, so it might be an option for a rainy day, even if you don't have kids. They are quite renowned within Russia and even booked abroad occasionally.