In the past we’ve flown into a city, had a few days there and then picked up the car to drive on to other place, handing the car back before spending a few days in the new place.
We did:
East coast: Boston>Pick up car from Logan Airport and drive to JFK>New York>Pick up car from Newark Airport and drive to Union Station>Washington DC (10 nights)
and west coast:
San Fran>Pick up car from SF airport>Yosemite>Santa Cruz>Santa Barbara>Santa Monica>Las Vegas>Grand Canyon>Santa Monica. (15 nights)
The only city where we really needed a car was Los Angeles, we found.