Karosta
Karosta was constructed at the end of nineteenth century as a naval base for the Russian Tsar Alexander III. After that it was a base for the Soviet Baltic Fleet until 1994 when the Russian army left Latvia. Some 140 warships and 30 submarines had Karosta as their base (source »)
Thus, Karosta is a really exciting place, with its mix of beautiful buildings from the Tsar times and remnants from the Soviet Navy era.
Today, Karosta is probably one of the most odd destinations in the Baltic States and a visit will defenitely not leave you untouched. Still today, just looking at the photos from a rainy Karosta, gives me the goosebumps.
Please note that Karosta is Ovcharka territory. Do not climb any fences! Never!