Tartu is a great city for students. Due to the fact that The area of Tartu is quite small, I'd say it doesn't matter in which neighbourhood you should live. Everything is so close and pretty walkable. But to be honest, the closer to the city center you are, the easier it would be for you, so think about these two regions: Karlova, Jaamamõisa. In the end it doesn't matter how far you are from the city center since the public transportation is also great. I wish you luck on your stay and enjoy the summer 