One of your first stops should be San Micheletto Complex. Here, you'll be able to find your bearings and get some great tips before you start exploring.
This tourist information center is often on the itineraries of visitors to Lucca Historical Center. But San Micheletto Complex isn't the only drawcard in the area. Piazza dell'Anfiteatro, Guinigi Tower, and Palazzo Pfanner are some other worthwhile sights close by.