Is it cheaper to rent at the airport or offsite?
In the car rental industry, airports are considered to be “premium locations”. So it is common to expect an extra surcharge to be added with the car rental fare for the convenience to hire the rental car from the airport.
Is it cheaper to rent a car at the airport or in the city?
Typically, it is cheaper to hire a rental car from the city (or even in the suburbs, as long as it is non-airport car rental). So if you are flexible with your transportation options, you can make the commute to the city and then pick up a rental car for a cheaper price.
Check out this story from Time magazine, which tells of one traveller saving almost $2000 by renting a car in the city instead of the airport.