There is an air-side hotel, I've never stayed but others have reported that it is acceptable. Suggest you make reservations.

There are two airside hotels, one in int'l term 1 and another in int'l term 2 (these terminals are essentially one big, connected terminal). They are on the 3rd floor in the passenger departing area and are operated by Louis Taverns/Miracle Grand. I've tried to get a working link, from the BKK airport site, but have not been successful.

http://www.miraclegrandhotel.com/dayroom.html

Note that there is a Louis Tavern hotel outside the airport too, this is a different and separate hotel from the air-side hotels.

If you head into town you'll have to clear immigration (twice, entering and exiting) and pay the 500 baht departure tax (once when exiting). All in all you'd have ~ 4 1/2 hours of sleeping if you chose to go into the city and get a hotel (factoring in clearing immigration, taxi, check-in, check-out, taxi, check-in at airport, clear immigration).

There are many all/late-night spots esp. for food, Ratchada comes to mind (which is not too far from the airport), which might be fun, but might be challenging to get to/from without local knowledge?