We stayed at Travelodge. It is the closest place to the airport. The locals know it as "el capital". We paid 84 dollars for the night. They have shuttles to the airport in the morning and very nice rooms. The taxi driver had plenty of cheaper of hotels to recommend, but we stuck with this one (recommend by immagration in bogota.) It is about 10 minutes from the airport.
Also there are a ton of atms on the departure floor.