You need not be overly concerned about the safety at the airport in EZE. There are a couple of ways to get to your hotel in the Cap Fed or any other barrio in the BsAs area.
The easiest is to go the EZE taxi counter just outside of the customs exit area. They will take your destination, give you a price and then you pay them and someone will escort you and you luggage to the correct car and give the driver the address. I have used them a lot and they are a very good service at competitive prices.
You can also get a taxi from one of the yellow and blck companies just outside of baggage claim. They are good, just make sure they start the meter or you get a flat rate. There is supposed to be flat rate charge to downtown, but you have to pay the tolls.
I wouldn't recommend getting a cab that just discharged a pax as it might cause a problem.
One other thing, only change money in the airport at the Banco Nacion, just outside of customs. It is open every day and it is the best rate you can get, the other cambios are total rip-offs. Enjoy a great trip in a beautiful city!