A good option for most people is Toronto Island. There are a lot of activities that can be explored there, including anything and everything you can do in a regular park, plus boating (cayak, canoe, paddle boat), bike rentals, and tons of activities and rides for the little ones. Now this overrated piece of real estate can be disputed whether or not it qualifies into the 'on a budget' theme. From the $42 for the park ticket rides (more than wonderland for a handful of kiddie rides?) to the $3 for the water bottle and $5 the super miniscule slice of pizza, you'll feel raped and sodomized pretty quick if you go in like a tourist. With a little planning though you can seriously cut down the costs and just enjoy the scenery. Boat/bike rentals are quite affordable and how hard is it to pack a lunch and bring in a bottle of water than can be refilled anywhere on the island?

FYI you can bring in anything from home that you can carry on your shoulders. That includes your own bike, roller blades, 6 ft cooler and grill, or Fido - the dog, not the cheap phone.