OP - would you care to mention the specific airport?
I know in some cities public transportation is a well-kept secret, yet indeed they have it. You might find you have an alternative with it you didn't even know?
In other cities, public transportation gets an undeserved bad rap, yet is very functional. I know lots of people in Florida will insist "Nobody rides Tri-Rail. It is always late." But I've used it quite a few times from various cities along the line to MIA, PBI and FLL. Successfully. Also have moved my body easily and safely about San Diego and Los Angeles, in spite of some dire warnings. It has been a while, but the last time I rode it, the Senior Rate for wherever I wanted to go was thrifty 75¢.
And another possibility - some hotels near an airport offer a "park and sleep" rate. For one night's lodging, you can also leave a vehicle in their parking area for the duration of your trip. I did this in Portland, OR where the deal was good for up to 14 nights. Again, a while ago, but maybe could work for you. Particularly if you are actually live quite a ways from the airport and a hotel night before or after would work well for you. These types of hotels also usually have shuttle to the airport and even breakfast sometimes.