We stayed in Callan Apartments at South Terrace & Jenkin Street. This location is fabulous between 2 free CAT bus stops, close to shops, restaurants and most importantly only one street and a short walk to the famous South Beach. We stayed a month and thoroughly enjoyed our time in Fremantle.
Across the road from the apartments is a fabulous restaurant called Bistro Monzu which is open for Breakfast, Lunch & Dinner. They are very friendly and their menu doesn't try too hard rather they let the produce and preparation speak for itself. Try the twice roasted pork - sensational!