You could take a bus to Coronado Springs, but there is no direct transportation to Downtown Disney from Studios or any other theme park, or vice versa. If you are relying on Disney transportation I would discourage using DTD if what you intend to do is leave the park, eat, then return to the park.
The closest resorts to DHS are the Epcot resorts and there is not a lot of counter service choice there. If you're on the dining plan, all you have is Hurricane Hanna's, the Beach Club Marketplace and the Boardwalk Bakery. If you're not on the dining plan, you can try the kiosks on the Boardwalk. I do not know what happened to Spoodles pizza window, since Spoodles is closed and there are no reports from Kouzzina yet. Also for those not on the dining plan, there is Picabu cafeteria at the Dolphin, which has better pizza than the Disney places.
The closest resorts by bus are Pop Century and Caribbean Beach, if you're interested in the food courts at either one. Keep in mind that Caribbean Beach has seven bus stops so that's going to be a longer bus ride.
Another alternative (assuming you have a park hopper pass) is to take the boat to Epcot's International Gateway and eat there, then take the boat back. (The boat ride from park to park takes about a half hour.)