On my opinion this is the best art museum in the city. It is located in the historical building and has a great collection of art. They have many great artist such as Vrubel, Rubens, Shishkin etc. They have a whole room with Ayvazovskyi's paintings.
If you are interested in visiting museums this is the place. It is situated near the city center (just 15-20 minuts walking). Enterence is really cheap. Pieces of art are worth coming. It is beautiful inside. )
They have 2 unique works of Ayvazovskyi.
Mon-Su: 10:30-17:30