If you really want to be cost-conscious, there are plenty of affordable hotels in Narita, saving you the train fare. (Assuming you're transiting NRT, of course)

There's a cluster of business hotels in Narita around the train station. You can take the local train from the airport to Narita for less than $2.50.

If you want to be REALLY cost conscious there are a few hostels. At 21, it's not a bad way to go. That's how I saw Japan when I was that age.

Keep in mind that NRT is quite a distance away from Tokyo. Even the fastest route from Tsukiji to NRT is over an hour.

OTOH, if you're transiting HND that opens up a few more options. At that point I might actually consider the overnight onsen option and even a quick breakfast at Tsukiji (maybe not the two famous places, but there are dozens of other restaurants open early without the lines in the outer market).

Also consider how tired or jet-lagged you might be, depending on your flights.