You are not asked that question in TurboTax. In the personal info section you are asked for your state of residence. Then you are asked if you lived in any other states. Do not enter states where you took basic or advanced training. In fact, military members answer no to the lived in another state question and only show their residence state (SLR/HOR).
Where the relevant question comes up, is on the parent's tax return, if they are claiming you as a dependent. And, again it does not ask where you took training. It asks how long you lived with the parent. The parent should count the time you were at training, as living with them, because it is considered only a temporary absence from their home.