If I'm already staying downtown I would probably stay downtown the night before anyway versus moving hotels (and probably wouldn't have a rental car either if I'm staying/working downtown and am either taking a taxi/Uber or public transit as needed around the city and to the airport). But a lot of my travels don't have me staying or working in downtown areas so the most convenient option is to get a hotel close to the airport, and I often drop off the rental car the night before and then either walk or take a shuttle to the terminal, depending on the options available at a given airport.