Not far beyond the stop for the castle on the 22/23 trams is the stop for the Strahov Monastery. When I went you weren't allowed to go in the rooms with the priceless old books but you could look in from a corridor. The ceilings of the two libraries are of outstanding quality and easily justify the three thumbs.
Address:
Strahovské nádvoří 1/132 Prague Hlavni Mesto Praha Czech Republic