Rather than having BBQ, Muar is famous for roadside eating specially in the evening, around two hotels: Streetview and Riverview. There are also several indoor dinning Chinese restaurants which I have recently tried - they are slight further away from the heart of the town, opposite direction of each other: Sin Kee Ting (Jalan Khalidi) and Chen Chen Siang (Jalan Bakri, towards Yong Peng).
The good hotels are Traders' Hotel, Hotel D99 and Classic Hotel. As for food you can get good food in the evening at this street called 贪吃街 or Gluttons' Street. You can get duck rice, oyster omelette and fish porridge. If you want to eat mee rebus or satay, then try the stalls near Traders' Hotel. You can view my video at this website:
At night a lot of local food also at Bentayan food center.