Quietly humming away in North Fremantle is Mrs Brown's Bar. Next door (and part of the company) to Flipside Burgers, Mrs Brown's is a relaxing place to sit back and enjoy a wine or beer and review the day.
If you sit near the front you can safely watch the "wildlife" which lines up for Mojos (2 doors down) - a great cross-section of the band going crowd. Alternatively you can sit in some comfortable lounges with your crowd and wonder about life (and where your burger is? - they deliver from next door if enough staff on duty).