You still haven't said where this is.
In my state, Ohio, in your situation your employer will withhold city tax for where their office is (it required by law). You can file for a refund, if you didn't actually work there (or didn't work there 100%). In most OH cities that takes a special form (you can't do it in TurboTax). Then you have to file forms and pay tax in all the cities you did work in, as well as your resident city. Contact each city for forms, there may be a minimum number of days exclusion.
Michigan cities are similar, but may not be exactly the same.
