What are the best things to do in Lucca?

Maybe start with the coverage here on the RS web site:

https://www.ricksteves.com/europe/italy/lucca

Links to recent travel forum posts re Lucca also on that page.

Tons of good restaurants in Lucca.

Try Cecina (salted chickpeas pie) from the oldest place around as well as other local delicacies like chestnut flour crepes.
https://en.pizzeriadafelice.it/from-felice/
Gelato with the best ingredients and unusual combinations - Gelateria De' Coltelli Via S. Paolino, 10 (just off Piazza San Michele)
Also really enjoyed Osteria San Giorgio and their charming internal patio Via S. Giorgio, 26

There are many churches - visit Basilica di San Frediano and see the patron Saint of Lucca.
Took a tour with the RS recommended https://en.turislucca.com/guided-tours-for-individuals/ and really enjoyed it.

Pisa and Pistoia are both easy direct train rides away for day trips.

Have a great trip,
=Tod

Agree that RS guidebook covers all highlights. But just enjoy the many piazzas and the wall.

Along with previously mentioned Osteria San Giorgio, I would suggest:

Osteria da Pasquale (our favorite)
Trattoria Canuleia
Ristorante all'olivo
Trattoria Gigi

Reservations would be needed at all of them.

If you're staying near the Guinigi tower, bistro piquet is good stop for coffee and food.

The Basilica of San Frediano to admire the Transportation of the Volto Santo

The Cathedral of St Martin for it's Façade, oh that Façade.

Oh, and how about that Façade on the Farmacia Centrale !

We really enjoyed renting bikes and riding on top of the wall and then around town. If bikes aren’t your thing just walking the wall is enjoyable as well.

Walk or bike on the wall surrounding the town. If interested, attend a concert of Puccini music, excellent! Here's a link: https://www.puccinielasualucca.com/home_en.html. We just love Lucca.

If you like Puccini, his old residence is now a museum in Lucca.