Day trip from Lucca: Parco Avventura
The Parco Avventura can provide you with a fun day trip from Lucca.
The parc itself is located in a forest in the Mediavale (the middle Serchio valley). It offers 3 percourses made of various rope bridges, between the trees.
You will find Parco Avventura 1h30mn North of Lucca, in San Romano en Garfagnaga. To get there you need to take the road toward Castelnuovo en Garfagnana (if Castelnuovo is not signaled, follow signs to Abetone), then after Castelnuovo go towards San Romano (you will turn left soon after Castelnuovo), there are signs to the parc right after passing the village of San Romano, to your right. See map.
The main attraction of the park are the 3 percourses in the trees, 2 for adults and 1 for kids (1m and above if I remember correctly, our son was less than 6 when he did it the first time). You rent a harness and a helmet, go through a simple session on what to do in the trees (pay attention though, if you don't follow the directions properly you will have to do it again) and voilà! You're off to the trees. You climb on the first platform, and from then on you go from one tree to the next using all sorts of different rope bridges. Instructors are always around, to help you if you need, or to remind you to follow the safety instructions. Kids are always supervised by an instructor.
The park also offers a nice (and shaded!) picnic area, with wooden tables, so when it's really hot in Lucca, it is still a nice place to spend the day even for those who'd like to stay closer to the ground.
And once you've enjoyed the trees, you can take a short (30mn) walk from the park to the 11th century Fortezza delle Verrucole, ask the instructors in the park for directions, it's fairly easy and you really can't get lost.