I can only think of a few restaurants inside a park that are open before the park. They are fixed price character or princess meals and require reservations in advance. The first reservation is at 8:05 for Crystal Palace (MK), CRT (MK), Akershus (Epcot), Tusker House (AK) and Hollywood & Vine (DHS). If the park has morning EMH, the restaurant doesn't open any earlier.
Rainforest Cafe at AK is just outside the park's entrance. I know they serve breakfast, but I'm not sure what time they open. Les Halles (France in Epcot) opens at 9 AM which is technically before World Showcase opens, although Future World usually opens at 9 AM.
There are also a number of restaurants at the resorts that open early for breakfast.