Residence of Bukovinian & Dalmatian Metropolitans by Luis Filipe Gaspar
I have visited the site just recently (July 2012). The whole residence is located at the end of University Street. Access to the place for non-students is possible with an organised group (so far Ukrainian only, costs 20 hr, 2 Euro). It last half an hour and covers short general introduction, reception hall, staircase, main assembly hall, former library, garden view from second floor and walk outside buildings.
I am not sure if it is obligatory but for sure it is the only possibility to see interiors of the buildings. As a part of complex a church (Greek Orthodox) is possible to see without any additional charge.
The whole visit should take approximately one hour.