We never really eat at QS at HS we have tried but good QS at HS is sorely missing. Sci-Fi is our spot for burgers and sandwiches, other than that we have grabbed breakfast pastry at starring rolls a few times to hold us over till lunch.
Over at Beach Club - you could go with Beaches and Cream soda shop, while this is a sit down option the burgers here are pretty good, and ice cream is really good. If your on the dinning plan you might want to pay OOP for this, its a fun time.
There is Splash grill and Picabu at the Swan and Dolphin, but if on the
DDP this would be another out of pocket.
You could boat over to Epcot if you have park hoppers, it will bring you in the back gate, as you are walking up the hill to your left is England, and wonderful fish and chips at the Yorkshire county fish shop, there are covered tables outside on the water when at the counter look to your left they are kinda hidden. If you turn right at the top of the hill is France and Les Halles Boulangerie Patisserie, and we enjoy their sandwiches and dessert. There are a lot of QS option at Epcot.
Also ESPN club might be a option if you are paying out of pocket, you could share some appetizers, then grab ice cream on the boardwalk for dessert. Our DD's loved doing this, they thought it was cool.
Hopefully once Star Wars land gets build and Toy Story land there will be some new and exciting offerings for QS at HS