Parking at any resort is free while dining or just visiting. You will be given a three hour parking pass when you reach the security gate and explain the purpose of your visit. If you have a dining reservation, have the confirmation number handy.
Some resorts, like the monorail resorts (especially the Contemporary) and the Epcot resorts, are very particular about parking due to the close proximity to the parks. Other resorts aren't that bad. Some security guards are more vigil than others.
In any case, have your driver's license and dining confirmation number with you and you'll be fine for at least three hours. After that, your car can be towed.