Jolimont Caravan Park, 30 minutes north of Mackay on the Bruce Highway used to be a lovely little park. Haven't been there for a number of years though. There is also camping at Cape Hillsborough just north of Mackay, another great spot. Seaforth is a lovely little seaside town to the north. I think there is a council park there.
Seaforth as suggested by "gypsy rover" (above) is about 50km north of Mackay, and yes, there's a council park, right on the beach, $95 per week (I think), large sites, unpowered sites only. You'll need solar as generators not permitted.
Also have stay at Jolimont caravan park for same reasons has Gypsy rover , if you want to be closer to Mackay the Showgrounds is open has well but have not stayed there