The City Bors, though technically separate, is in effect an annexe of the The Hamburger Bors, where reception and breakfast are to be found. It is diagonally opposite to the Hamburger Bors at traffic lights and adjacent to the market. It's cheaper than the Hamburger Bors but the en-suite rooms with TV and phone are excellent.
If you are intending to stay in Turku on your way to and from the Åland Islands with the Viking Line, they or their agents in your country can probably get you a real bargain rate.