Response: After you travel to Forest Gate, the first player may draw 2 cards.

What does exactly mean? That after you finish adding 4 tokens on the active location and before discarding it, you can draw 2 cards? Or you can draw 2 cards when you move the location from staging are and make it active?

You can draw 2 cards after you choose to move the location from staging and make it active during the Travel phase -- this is when you "travel". There are player cards that let you make a location in staging active without actually travelling to it, and using those would not let you use the response.

If it read "Response: After you explore Forest Gate, the first player may draw 2 cards", then you would draw cards after you finish adding enough tokens on it to be able to discard it. It would not matter if you placed those tokens on it as the active location as a result of questing, or placed the tokens with cards such as Northern Tracker or Snowbourn Scout.

Thank you!