One of your first stops should be Goondiwindi Visitor Centre. Here, you'll be able to orient yourself and get some great tips before you set out exploring.
When you've finished at this Goondiwindi tourist information center, why not check out Goondiwindi Golf Club, Goondiwindi Natural Heritage & Water Park, and Goondiwindi Riverwalk Trailhead? They're not far from Goondiwindi Visitor Centre and also a hit with travelers.