There are many options for accommodation in Bangkok. From the Don Mueang airport itself or Suvarnabhumi lute there are many more expensive and cheaper hotels or guest houses.
You can make reservations through the hotel booking websites. There are home small hotels with a few rooms to rent, there are cheap 2 or 3 star hotels. Well you can find many 4 or 5 star excellent hotels. In Bangkok you will find well-known hotel brands as well as many great Thai private companies.
Hotels can be reached by public transport, sometimes hotels offer their transport or you can take advantage of a professional private transfer by minivan or limousine at ThaiTransfer