For a couple of days I wouldn't plan too much. Walk the walls or rent bikes or the group bike cab and circumnavigate the walls.
There are five climbable towers in town and there is a river path for biking and you can go as far as Pisa if you want to. September is traditionally the month the weather breaks so it may still be warm during the days.
Best local pizza experience - Pizzeria da Felice - always packed and spilling into the street outside with little quarter given to tourists. Run the way it always has been with pizza and cecina sold by weight. Try the cecina with the pepper when offered.
Probably better pizza but less of an experience is Itaco across town.
Best gelato; Ele (formally De' Coltelli) and Momo in either location. There are other good places but these are the best - ele for wacky combos and amazing fruit flavors.
Best sandwich place: Ciacco on P.za Napoleone. If there's a crowd waiting just check in with the person running the front and she'll get to you in order - just trust the system.
So many good restaurants - always safer to make a reservation if you really want to eat someplace specific. Piazza dell'Anfiteatro is beautiful and worth wandering through at night but is for tourists not locals. If you want to make that scene Sotto Sotto has the respect of the locals so I'd eat there.
There are musical performances every night ranging from free to expensive opera all over town but especially in September. Check the various websites but also look at the fliers around town. The Grapevine magazine calendar is a good place to start: https://www.luccagrapevine.com/
Example schedule: https://www.luccagrapevine.com/february2025/WO.pdf
https://eventi.turismo.lucca.it/en/
A fun BnB with some slightly over the top rooms is La Boheme if that interests you. It's very much in the center of town.
https://www.boheme.it/en/
In Lucca, as in Italy, they respect the siesta and la domenica so expect closures in the middle of the afternoon and on Sunday with some places tacking on Monday as well. Plan accordingly.
Have a great trip,
=Tod