Sevastopol is a good jumping-off place to see some of the sites from the Crimean War. There is an amazing museum called a Panorama, which depicts the siege of Sevastopol from the Russian point of view with a display a little like a diorama, but much more impressive - there is a huge circular canvas of about 2000 square metres as a backdrop, and then lots of props such as cannons and models of redoubts in the foreground. It's narrated in Russian but you can hire an audioguide in English or French. Admission 40UAH +25UAH for camera.
There is a park with war memorials on Sapun Gora nearby, though it focuses on the battles of the World War Two siege of Sevastopol. You can visit the "Valley of Death", where the famous Charge of the Light Brigade occurred, and you can also visit nearby Balaklava, site of another famous battle, and an interesting little town, formerly a Russian submarine port.
The Greek city of Chersonessus is located about three kilometres from Sebastopol, near the city centre; admission is 40UAH for Ukrainians plus 15UAH for a camera, and 60UAH for foreigners camera is free outside, though if you speak Russian and argue you can get in for the Ukrainian price. There is a good guidebook available from the ticket office for 15UAH. This is where Volodymyr, the first leader of the Kievan Rus to convert to Christianity, was baptised; there is a large cathedral at the spot, rebuilt in 1999 after being closed down by the Soviets in the 1920s and blown up by the Nazis in 1944. Also on the site are various Byzantine basilicas, including a famous one with marble columns, and the 'foggy bell', made of melted-down Turkish cannons in the late 1700s, which was taken to Paris after the Crimean War and returned in 1914. Tourists swarm all over the ancient monuments with little respect for their antiquity. Few signs tell you what is what. Still, the atmosphere is nice. Consider bringing your swimming gear - the locals do, because there's a narrow but beautiful beach located in the grounds.
There are many Soviet war memorials - Sevastopol is one of the thirteen Hero Cities of the Great Patriotic War. There is a large statue of Lenin, with soldiers, peasants and workers, on ul. Sovietska which is the spine of the main section of the city. There is a statue of Nakhimov, who defeated the Turkish fleet and masterminded the defence of Sevastopol at the time of the Crimean War, in a square at the head of the main part of the city.