Off the top of my head and not checking anything on Wikipedia or looking at the other responses – honest!
Queen of the South: Dumfreis
Queens Park: Glasgow (Hampden Park)
St Mirren: Paisley
St Johnstone: Perth
East Fife: somewhere in Fife, presumably near St Andrew’s.
Hibernian: Edinburgh
Heart of Midlothian: Edinburgh
Cove Rangers: Aberdeenshire
Spartans: Edinburgh