Couple of things--

(1) taxis will be about $20-30 into various parts of the city, maybe slightly, but not much more unless you're headed out to Woodlands or something... there's never a wait for a limo at night, so no need to prebook those and at a flat $35, they are a good deal after midnight when the night surcharge is in effect (or when the taxi queue is long, which is typical on, say, a holiday wknd).

(2) 803 is NRT-SIN and 896 is SIN-HKG, just so you don't take the wrong flight!

(3) LoriQ's suggestion of the transit hotel is interesting, but there are a few problems with it: if you want to use it on arrival into SIN, you need to have an onward ticket to somewhere else in the morning, otherwise you're technically not eligible to stay (not sure if they enforce it or not, but they're usually too full not to); furthermore, you cannot go out and pick up your bags and then go back in, so your bags would have to be checked through to your onward destination; if you want to use it the night before you leave, you'd need to somehow have your boarding pass already to get through immigration. given that OLCI is not available from non-US destinations, not sure how you'd get that for 896 unless you were connecting from another flt in which case that airline might be able to print it for you.

let us know if you have other questions on SIN-- lots of expertise on this and other boards.