the Conrad Cartagena is a lovely hotel with a awesome rooms, no executive lounge and great restaurants but there is nothing to do near by. the old city is a drive away and the hotel taxi charges $20 USD (one way)
The Hilton Cartagena is a dated property in need a comprehensive remodeling job but it is within a walking distance to the old city and if you don't want to walk, the taxi will cost you $ 2.5 USD