The museum itself is quite nicely placed in the old Carmelite cloister and lapidarium. An additional extension from the 1980s adds space for administrational and functional areas.
I didn't have time to explore Frankfurt in depth but what I saw from walking from the train station to the museum was not exactly overwhelming; even the cathedral was very plain and unimpressive.
This is the Ratskeller, a restaurant within the 'Römer' (name for the city hall):
Frankfurt cathedral, reconstructed in the 1950s after it had been almost completely been destroyed during WWII:
The most precious relic of the cathedral is the skullcap of the apostle Bartholomew. The Bartholomew relief by Hans Mettel from 1957 on the northern wall of the cathedral probably depicts the flayed apostle:
A stained glass window in the cathedral:
A Gothic tomb slab, now set into the wall of the cathedral, showing the mayor of Frankfurt, John of Holzhausen († 1393) and his wife Guda Goldsteyn († 1371):