Edited to add: We don't sort out accommodation when we're
on duty. AJX provides accommodation when downroute and when we're in Japan for duty e.g. simulator.
When we're
off duty:
You receive $550 per month accommodation allowance. If you are on standby and do not get called then you will receive an 'extra' $55 to cover the additional accommodation.
If you choose to stay in MyStays Hotel you will pay JPY7000 per night. There is an amazingly complicated formula where they calculate if the exchange rate etc covers your accommodation and if you get additional money but no-one actually understands it. Sometimes extra money appears on the pay slip to cover the above
Some people choose to stay in Narita apartments, which are cheaper than Tokyo and closer to commute to the airport (assuming you're not rostered to fly from HND). Apartments are usually around the JPY80000-90000 per month mark, including utilities. Some people have their own, single, apartments and some share slightly larger ones. If you think of around JPY80000 for a single and JPY50000 for sharing then I reckon you'll be able to calculate if you'd like to do that or not.
I don't know how much the guys in Tokyo pay but they will be more expensive. They get to enjoy the proximity of the sights and sounds of Tokyo itself, instead of Narita, but will have to endure the extra time on the train/bus most of the time commuting to NRT for duty. Sometimes they will fly from HND and there commute will be greatly reduced but that will be in the minority and the schedulers don't care where you live.