The airport is about 30 to 40 minutes drive away from the central districts of Bangkok. There is probably a few airport hotels, but since it only costs about 300 baht (about $8 USD) by taxi to the city I recommend you head down town for the night.
You could either head for the Sukhumvit area (fancy hotels for 1200 - 3000 baht a night) or Kao Sahn Road (the backpackers area, for 500 - 1000 baht per night). Both have interesting nightlife any day of the week!
If you want to book in advance then check out wotif.com as they have a good variety of hotels listed for Bangkok. about 10 years ago
Watch out for traffic during rush hour if you're headed back to the airport from town. I had mates who missed flights cos they didn't factor in the 2 hour traffic jam in the middle of town.
If your flight is not too late your best bet would be sleeping overnight at the airport. Thailand is relatively safe. almost 10 years ago
I have stayed at the Queen's Garden Resort, whcih is only 10 minutes from the airport. The place is very clean and comfortable, and very affordable. They will come pick you up and offer free shuttelbus service one-way (if you book online).
http://www.queensgardenresort.net/ over 9 years ago