There are a lot of great places to visit. You could go to the many surrounding shopping areas, you could go to Old Town, Downtown Disney and City Walk are great and can be free. You could take a drive and go to several different places, or even head to the beach.
As far as something like a park that is free, this is going to be a little harder to find. I like places like Wonderworks and Ripley's and Hard Rock Vault, they are less expensive than a theme park, and just as fun. You could also go to water parks, putt-putt golfing, arcades, etc. There is a lot to do there outside of the theme parks.
But to get free tickets to Disney the only way to do this is to do a timeshare tour. The best thing to do is to look online to see if there are any discounts, just do a search, you will find lots of information. If you don't find anything good, you could always wait until you get there and use the coupon books that you will find everywhere.
Hope this helps