I went for its tower but ended up loving the Duomo.
Almost all, if not truly all, visitors of Pisa went for the world-famous leaning tower, but surprisingly even if there is a crowd outside to pose with the tower, very few people seem to notice the much bigger structure nearby that is also the reason for the tower's construction: the Pisa Duomo, or formally Catedrale di Santa Maria Assunta!
Dedicated to the Assumption of Mary, the Pisa Duomo was the answer to compete against the then-reconstructing Basilica di San Marco in Venezia when both Pisa and Venezia were competing maritime powers. As a display of power, the then-powerful Pisa built this grand cathedral complex combined with the largest baptistery in modern-day Italy and of course the famous (unintentionally) leaning bell tower - right outside the city wall also as a show of confidence.
The result is an uniquely beautiful cathedral that is a blend of various architectural styles from various parts of the world, like the internationalism of the then Pisan merchants. On the outside, the white facade is fantastically adorned with detailed sculptures and reliefs of many tales. Inside, it's an elegant yet ornate cathedral that is truly unlike others, especially with the beautiful striped arches that flank the sides and the Renaissance-esque ceiling that was forward of its time. Although this cathedral never matched with San Marco's extravagance because of waning Pisan power, it is nonetheless a worthy competition of beauty to the Venetian basilica in my opinion.
In the end, this church was actually my favorite part of Pisa and also one of my favorites in the world, and it is a shame that only a small fraction of the tower admirers stepped inside this "hidden gem" especially when it's free. If you are already making your way to go to Pisa, why not take a step into this gorgeous cathedral?
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ADMISSION:
The admission to the cathedral is free, whether you purchase admission to other sights in the Piazza or not. All you need is to get a "timed ticket" at the ticket counter in the building south of the Baptistery.
The entrance is technically timed, but I don't think the door staff won't care because it's never full inside.
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HOW TO REACH PIAZZA DEI MIRACOLI (https://www.yelp.com/biz/piazza-dei-miracoli-pisa?hrid=R9FEXF6UDKph9lvD8yeWVg)
The easiest train station to reach is Pisa Centrale, although the smaller Pisa S Rossore is only a 5-minute walk away from the Piazza. Centrale may be better because more and faster trains pass through it.
From Roma, you can directly connect to Centrale via a 2.5-hour Frecciabianca ride.
From Firenze, you can directly connect to Centrale via a 1-hr "Regionale Veloce" (1.5 on regular Regionale) ride.
From Pisa Centrale, you can choose to 1) walk 20 minutes or 2) take the 10-minute LAM Rossa bus. I recommend taking the bus because the fare is only €1 with a 4-ticket carnet from any newsstand and the rest of Pisa is dull, but beware of the pickpockets.
Since you have to transfer at Pisa Centrale for Cinque Terre (unless you are directly going to La Spezia from Roma), why not make a Leaning Tower stopover?
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tl;dr version:
1) The main reason why there is a Leaning Tower to begin with!
2) Uniquely beautiful cathedral that is ignored by many
3) If you're already in Pisa, why not enter for free? read more