Hi, Kartik!
Although it's rare to find cheap hotels within any international airport, here are some of the options that you may want to check out at the Bangkok airport:
1. Suvarnabhumiville Airport Hotel
2. Miracle Transit Hotel
3. Miracle Suvarnabhumi Airport Hotel Else, you can check with immigration officials whether you have to purchase a Tourist Visa or will your passport allow you to leave the airport for a short while with a free Visa exemption? If that's the case, you can check out the city or get a cheaper hotel outside the airport.