Dec31/Jan1
Dec 31 - most supermarkets will be open until 18, some specialty stores will be open until 16, the small retail shops like Zabka may be open up to 23
New year 01.01 - most shops will be closed that day, only few will be open, like some 24 Hour Delis and small retail stores where the owners will be sitting behind the cash desk.
Słowacki Theater
Open - slowacki.krakow.pl/en/repertoire/large_stage/_get/month/12/year/2016
19th Century Polish Art Gallery
Open Dec 31, closed 01.01 and all Mondays
Cloth Hall (Sukiennice)
Same as Art Gallery above
Town Hall Tower
Closed between November and March
St. Mary's Basilica
January and February closed, the other months open for visitors from Thursday to Saturday 9:10-17:30 (entry every 30 minutes) - In the case of bad weather the tower may be closed
St. Francis' Basilica
It seems to be open weekdays 10:00 - 16:00, on Sundays and public holidays: 13:00 - 15:00.