Well if you are in Sevastopol you have to visit the Port. It's what Sevastopol was/is all about. During the Soviet reign Sevastopol was a 'secret city' I think they called it. It harboured a big part of the Russian fleet. Only people who had to be there, ie military people, were allowed there. As a consequence many of the older houses have been preserved and Sevastopol does not have any of the worn down concrete buildings that is so typical for many other Russian cities.
There is a lot of night life and decent restaurants along the harbour and so it is the place were most of the young people hang out in the evening.

Take a boat to the open air museum of the soviet union naval fleet, and admire the great ships of the soviet union and russian fedderation.