Any recommendations ?
The airport is pretty close to the center and easy to get to in about 40 min-, so you could just stay in town depending on your flight time.
https://www.pisa-airport.com/en/the-passengers/transport/people-mover.html
We always stay in Lucca, very pretty town. Quick, easy trip to Pisa airport.
https://hotelbologna.pisa.it/en/
AND they offer a free shuttle service to and from the Airport.
AND they serve Caperberries at the bar as part of their snacks.