This is just a few to get you going. There are many cafes for coffee and rest breaks.
Alexandra Park Zoo (free)
https://www.discoverbundaberg.com.au/alexandra-park-zoo
Botanic Gardens (free)
https://www.bundaberg.qld.gov.au/botanic-gardens
AUSTRALIAN SUGAR CANE RAILWAY, BUNDABERG Adults $6 selected days
https://www.bundabergcanetrains.org.au/
Hinkler Hall of Aviation $24
https://www.discoverbundaberg.com.au/hinkler-hall-of-aviation
Fairymead House Sugar History Museum $10
Peace Pole (Lions Project) (free)
https://bundaberglions.com/bundaberg-lions-projects/parks/bundaberg-lions-peace-pole/
Rats of Tobruk and Lions Remembrance Park (free)
https://bundaberglions.com/bundaberg-lions-projects/parks/rats-of-tobruk-memorial-park/
Walk on a Beach (free)
Take your pick there are several.
Original Burnett Heads Lighthouse a major landmark (free)
https://www.artsbundaberg.com.au/downloads/file/26/historic-burnett-heads-lighthouse-story
Bundaberg Brewed Drinks (Ginger Beer) The Barrel (free to visit shop)
VISIT THE BUNDABERG RUM DISTILLERY (free to visit shop)
https://www.bundabergrum.com.au/distillery/book-a-tour.html
Macadamias Australia Visitor Experience (free to visit shop)
https://visit.macadamiasaustralia.net/
Hummock Lookout (free)
https://www.queensland.com/au/en/things-to-do/attractions/p-56b265782cbcbe7073adf4ec-hummock-lookout