Victoria Park is an easy 10 minute walk from Goulburn station and has an excellent outdoor gym on Faithful Street.
If you're a fan of outdoor gyms you'll like this one. It has instruction plaques and recommendations with each one, useful for planning your routine. There's a stretching station to help you warm up and warm down, stepping equipment, parallel bars, an exercise bike, benches for stomach presses, an eliptical trainer and equipment to work out your thighs, arms and back.
This Community Gym is set on a soft fall area, dappled with the shade of many mature trees for most of the day. So it's a comfortable place to exercise most of the year around, and if you bring your kids you know they won't hurt themselves if they fall over.
There's also filtered water available at this spot and if you want to make a day of it, there are barbeques, toilets, outdoor tables, a children's playground, an off leash area for dogs, an aquatic centre and a duck pond all within the park precinct.