Yes, you have to use 'to' in these questions. It is not possible to omit it.
You go TO a place. The only exceptions are when you use 'go' with an adverb such as 'upstairs', 'downstairs', 'away', 'abroad' and 'home'. These adverbs include the idea of movement in a specific direction, so there is no need to use 'to' with these words. But if you name the place (the name of a town, country etc) or the type of place (a butcher's or a school or an airport), you always need to indicate movement with a preposition before the place.
You also don't need 'to' is if you use the word 'where'. This is because 'where' includes the concept of movement towards a specific location. For example, you can ask "Where did you go?" or "That's the place where I went."
I hope that helps.