It was a fantastic tour of the inside. The National Museum of San Matteo, which is housed in the Benedictine Monastery, features a group of paintings from the 12th- to 18th- centuries, and a rich collection of sculpture from the Pisano School. The sculptures were absolutely wonderful, but not to be outdone, the paintings were well presented and preserved. It really is a library beside being a museum and the university right close to it uses the facilities for research.
Other places to see if you have time (which I didn't) are the Museums. Here are some to take note of.
Cultural Institutions: S. Matteo National Museum (Tuscan sculptures and paintings of 12th to 15th centuries)
Museo delle Sinopie
Scuola Normale Superiore.
Nice small museum, entrance is covered if you buy the climbing tower tickets. Won't take long to walk through. Contains a few antiquities from Greece, Romans and Egyptians.