Flights to BA
All major US airlines, and several international ones (E.g. Iberia, Air France, ITA, Emirates, Lufthansa), fly to Buenos Aires.
The two main airports are: Ezeiza (EZE - most international flights land here) which is about 1 hour away from downtown, and Aeroparque Pistarini (AEP - only domestic and international flights from Brazil or LATAM flights with layover in Santiago or Lima land here) which is ~15-20 minutes away from downtown.
Domestic flights primarily depart and land in AEP (e.g. to Mendoza) as well as some flights to neighboring countries such as Chile and Brazil.
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Airport Transportation
There are a few options to get to your hotel:
Arrange directly with your hotel - may be a bit more expensive but usually high quality and highly reliable.
Use services such as Airport Transfers in Buenos Aires from Viator or Blacklane.
You can also book directly at the airport - if you decide to do so, please use branded offices inside the airport (safest, most reliable) such as Manuel Tienda Leon. These are located in Ezeiza before the welcome hall and in Aeroparque in the arrivals hall.
Cabify and Uber are not viable options even if they state so (not allowed into the airport)! Also, not recommended to book taxis or “remises” on site (e.g. from someone offering them in the welcome hall).