The Püspöki Palota — the Bishop's Palace — is the grandest secular building on Castle Hill, a long baroque façade facing onto the main square at the southern end of the ridge. It was built in the 1760s by Bishop Ignác Koller as a residence in the style then common to Habsburg episcopal courts: long sequence of state rooms, decorative ceilings, formal reception spaces.
The interior is open for guided tours that take in several of the state rooms and the small ecclesiastical museum. Even from outside the palace is worth a stop — the façade dominates the cathedral square and the views from the terrace behind it run out over the valley.