IIRC a Roppongi all-nighter will easily make a bigger dent in your wallet than a low-budget hotel room... not that I've tried either option recently. I do agree that partying all night would be a fun way to handle the hangover (oops - I mean layover) if your flight times and your constitution will allow it.

I think Narita is a fair option too for a first timer. Really there are so many choices - Narita CIty for a "Japan" experience right by the airport / Nippori area for "classic" working class Tokyo / Roppongi all-nighter for kicks / Ginza, Omotesando, Roppongi Hills for a taste of high-end Tokyo / Shibuya or Shinjuku for a blade-runner neon dream... any one of those would be a good way to spend 18 hours.