Today Disney tweeted that guests will be able to park in the Lemon or Grapefruit lots for a premium starting June 1st. The two lots are the closest to walk directly into Disney Springs. The Lemon lot is located next to the Marketplace in Disney Springs, and Grapefruit is next to the West Side. See the Disney provided map below.
Disney Springs will continue offering free and valet ($20) parking as well. Parking can become an issue during busy weekends and holidays. Disney is aware of the issue and is currently in the process of building a third parking garage to help alleviate the issue.
During busier times guests sometimes have to park behind the old Suntrust building and next to Casting and Team Disney.