Suvarnabhumi Airport is busy all night, and as there is no public transport that operates all night or takes you to early morning departures, the most convenient option may be to stay overnight at the airport.
Hotels at the airport
At the entrance to the train station you will find two capsule hotels , the Boxtel @ Suvarmanhumi Airport and the Avagard Capsule Hotel. In these accommodations, you'll only have a cramped enclosed space with one bed to yourself. In these capsule hotels, there is no shower facility and the toilets are for public airport use only. Prices are around 37 eur per night.
The only normal hotel right on the airport grounds is very good Novotel Bangkok Suvaranbumi **** with prices around 139 eur per night for 2. The general public not staying at this hotel can also use the pool, gym and sauna for a fee 800 thb per day.
Hotels in Bangkok
If you prefer to stay right in the city centre, there are a wide range of budget hostels for a few hundred baht and luxury hotels of international brands.