"I lost my wallet. I will go to the police box."
I think the Doctor has better things to do then go back in time to retrieve your wallet!
Just watch it unfold so that he stole his own wallet from his past self and that's why it went missing in the first place. What a twist...
へ is used more when one is going in the general direction of i.e. カナダヘ vs カナダに = towards Canada vs to Canada. へ is for direction, に implies destination. They are often interchangeable unless you need to specify.
Important: the "police box" that こうばん is referring to is not the British type. Japan actually has "police boxes" that are little buildings with a few policemen in them. These are こうばん.
That feel when you verbally translate it correctly to yourself but accidentally switch up the ます and まし tiles and get it wrong (;_;)