I believe police boxes in Japan are often used to ask for directions from police officers. It's not easy or common to ask other people on the street for directions and the police will have a map to give you the best route.

Apparently so. Wikipedia says that "as of 2007, there were about 6,000 kōban all over Japan". Also, here's a quote from the Japan National Tourism Organization:

"Your best resource for contacting the police, getting directions if you are lost, or for reporting a lost or stolen item, is your nearest “Koban”, or police box. This network of mini police stations is unique to Japan, and they can be found in virtually every neighborhood throughout the country, there are over 1200 Koban in Tokyo alone. While not all Koban are staffed 24 hours a day, most of the police boxes located in heavily populated areas will have an officer on duty."

To illustrate, here's a picture of one:

I guess the Doctor visits Japan a lot.

Probably the translation to Police Box remained from the time when they were in use in Britain, but they are not actual police boxes, but rather just small police stations

I came here for the Doctor jokes.

This is one of those things where it probably takes a lot of study and immersion in Japanese before you get a natural feel for which is right in a particular situation, and how using one or the other subtly changes the sense of what you're saying

Anyhoo, は is more for establishing the topic or setting a new context. So it's like "police boxes - are there any nearby?". Whereas が is more like talking about a specific thing, where you might use it or the in English. "Is the police box nearby?"

I mean obviously I'm still trying to get the hang of it myself, but it feels more natural to me to use は here

I agree with telemetry, but here is a tip for you. You will almost always find は marking the topic or subject of a negative verb.

England

Do a Google image search for police box in Japan. As others have noted, they're basically little tiny police stations. They're actually very cute

A small police station. There is one in most neighborhoods.

I lived in Japan for 2 years. I think that's a very appropriate way. To the point and respectful of their time.

すみません、ちょっといいですか？ Should be fine for most situations when asking questions to a stranger on the streets.

I put near as well. There is a difference between near and nearby, where near is used for comparison (with far) whike nearby is the grammatically correct to describe distance. Or something like that.

Im not sure I've ever heard a kouban-type place referred to as an office. It's really more of a small station where you can go for help, whereas an office conjures imagery of filing and booking and such, at least IMO

"Vacinity" is a typo. It's "vicinity".

Any police box would 交番でも, a police box would be more appropriate.

"Are there any police boxes near here" would be grammatically correct