If you can visit Pisa on a separate day trip, I would do that --- there is so much more to Pisa than the tower, plus Lucca would not seem so relaxing and friendly if you had to rush off to another place!
We spent 6 nights in Pisa and pretty much ignored the tower except for its exterior and liking to watch people trying to get a funny photo of it.
In the Field of Miracles
Duomo
Battistero di San Giovanni (door & tops of inside columns with beasts & monsters, sculptures inside)
Camposanto (my favorite with such interesting frescoes and its history)
Museo delle Sinopie del Campo Santo --- drawings for the 12th & 13th century frescoes
Opera del Duomo Museum
Plus have a snack and see the view at the + 3.9 Caffè Panoramico (open until 8pm, must book)
Interesting churches
Santa Maria della Spina
San Piero a Grado .....20 mins by bus --- Deodato Orlandi frescoes: https://www.flickr.com/photos/cienne/sets/72157600114508041/
San Paolo a Ripa d'Arno and behind it is Cappella di S. Agata (8-sided)
San Francesco --- 13th century frescoes
Santa Caterina facade
San Sisto, Santa Cecilia, San Silvestro --- Islamic ceramic bowls on exteriors
San Michele in Borgo --- writing on the exterior stones
SS. Felice & Regolo, via Ulisse Dini, ancient Roman capitals
Interesting museums
Museo Nazionale di San Matteo --- history of Pisa, sculptures from cathedral, 12th & 13th century paintings including Nicola Pisano, Donatello, Simone Martini, & Fra Angelico
Le Navi Antiche di Pisa --- naval museum: https://www.wanderingitaly.com/blog/article/1184/historic-ship-museum-pisa?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+WanderingItalyBlog+%28Wandering+Italy+Blog%29
Gipsoteca di Arte Antica --- nicely weird gallery of plaster casts of famous sculptures
Egyptian museum --- Collezioni Egittologiche
Interesting things to see or do
3 km walk on top of Pisa's city walls, book a visit: https://www.muradipisa.it/organizza-la-tua-visita/#orari
Botanical Garden
Domus Mazziniana --- literally has writing covering its exterior wall
Piazza Chiara Gambacorti, locals call it Piazza della Pera
Vettovaglie Market open daily (except Sunday) 7 a.m. till 3 p.m.
Palazzo della Carovana facade (in P. dei Cavalieri)
Half-day trip to Museo Piaggio --- open Tuesday to Saturday, Voluntary 5 euros/each. 20 mins by train. Must book online.
Other leaning towers in Pisa:
*San Michele degli Scalzi --- bell tower tipped at a five degree angle
*Guelfa Tower --- there's a view if it's open