At normal hours of the day, there are numerous airport buses that go on past Tres Cruces towards the old city and actually let you off a block or two away from the Radisson. I don't know if they run all night, though.
I'd just ask either a bus driver or some other passengers if there's a bus that goes by there. I'm pretty sure there's no need at all to take a taxi. Save the extra cash for a chivito
