Personally, I wouldn't be out on the road in the wee hours for security reasons and would just hang around the airport until daybreak which is only a couple of hours after your arrival this time of year.
You can use Taxi ezeiza - served inside airport to buy transportation to any hotel you wish to go. The drivers are vetted and very safe. However, you must go to a major hotel which the driver can easily find.
Also, avoid going to a hotel on Florida street as it may involve walking in the dead of the night with luggage.