If you are looking for a hotel near the airport, you have multiple options in different price ranges. Most hotels have a free shuttle service, so you can easily get to and from the airport. The shuttles leave at the airport bus parking at level 0.
Hotels that do not offer a shuttle service are easily accessible by public transport or by taxi. Do you prefer to stay at the airport itself? That is possible at the Sheraton Hotel, right in front of the passenger terminal. The only thing you have to do in the morning to catch your flight is to cross the street.
This is a list of hotels in the Brussels Airport area. Hotels with an asterisk offer a shuttle service to and from the airport.