You shouldn't have a problem. In past years, Disney has really stepped up its game. It's no longer your typical "theme park food."
Here are my top picks around the world:
Disney Springs: DS has become a hotspot for foodies. Tons of great offerings for fickle eaters and adventurous foodies:
Wolfgang Puck Express—pizza is good (coming from a NY'er) and can easily serve two people. They also have a stellar selection you wouldn't expect from a "fast food joint" such as bacon-wrapped meatloaf, Oven-Roasted Salmon and Half-Rotisserie Chicken.
D-Luxe Burger—A burger spot? Yeah.. a burger spot. These burgers carry a hefty price tag, but you really get a bang for your buck. The burgers are colossal in size, juicy and topped with an array of fresh ingredients.
Magic Kingdom: Columbia Harbor House is great for lunch and/or dinner. BOG will likely require an ADR for lunch/breakfast
EPCOT: So many options to choose from. A favorite here on the DIS is Sunshine Seasons, which is known for its fresh and above-average offerings. We also enjoy the QS in Japan.
DHS: Skip it. Head over to Boardwalk Bakery, instead. On top of all the delicious baked goods and confections is an assortment of freshly prepared sandwiches. Such a good spot for breakfast or lunch.
Resorts: We really enjoyed Landscape of Flavors over at AoA. Contempo Cafe at Contemporary, Capt. Cooks at Poly and the food court over at POR is also very good.
Really, timing is everything. If you go for dinner at 5pm, you're gonna wait for a table. Always secure a table and leave a family member (if possible) at the table before ordering. We've all been stuck, tray in hand, scanning the room for an open table. It's not fun.