------(What, Where) is Kate going? To the cinema.

应该 where
回答用的 to the cinema 是地方 所以 是where
如果回答是 to cinema 就用 what
如同 in hospital 是病了看病 in the hospital 是去医院不一定是看病
1.
——Where are you going?
——To the school/ the museum/ the library.
2.
——What are you going to do?
——To school/ dance/ swim/...