First - Singapore would be a better place to be arriving at midnight than Japan for sure, you wouldn't really struggle to get around and a taxi to a hotel would be simple. Singapore is, to a fair degree, a 24/7 city. If you do want to see the waterfall it is going to be a lot more fun at 2pm rather than 4am (the bus is a lot less frequent to get there)

However, the answer is fairly simple - there is literally only one oneworld flight a day that goes NRT-SIN, which is the one you're on. So, unless you change your trip to go to HND (2 flights a day at 0:10->06:40 or 10:55->17:25), or go via HKG (lots of flights at all times) you will just have to manage the late arrival:


See the flights (excluding codeshares, i.e. bare metal)

So then you get down to a hotel - you could get an expensive one at the airport (or in it), but most people would go downtown to get to a hotel in their budget/price range, and enjoy the city. For that it really is best discussed in the Singapore travel forum - but personally I would go to a hotel and see the city during the day. There is a lot less transportation and things to do at 4am, and a hotel will charge you for a night unless you're checking in at ~2pm (typically) unless you find a place that charges by the hour.