Hello Roxanne!
Thank you for your compliment on the panel!
I have to say, that your choices for breakfast in the parks is pretty limited. When you say that you're looking for a "nice" restaurant, I am going to assume that you would like a table service and not a quick service location. If this is the case, you only have one option each at Epcot and Hollywood Studios and they are both character meals.
At Hollywood Studios breakfast is served at
Hollywood and Vine and it is a buffet. The characters are from Playhouse Disney and include JoJo, Goliath and Leo and June from the Little Einsteins.
At Epcot your table service breakfast option is
Akershus which features various Disney princesses. This meal has a cold buffet line where you can choose fresh fruit and pastries. Then your server will bring a hot plate to the table which is served family style which contains scrambled eggs, potato casserole, bacon and sausage.
There are a few counter service locations in each park that have a limited breakfast menu, but they offer the same items that you would find available at your resort quick service.
If a character breakfast buffet isn't what you had in mind I would suggest booking an early breakfast at one of the resorts close to the parks that has a table service breakfast option. One restaurant that comes to mind is
Captain's Grille located at the Yacht Club. This restaurant offers a breakfast buffet and a la carte options, and there are no characters to be found. Afterwards you can either walk or take boat transportation to both Epcot and Hollywood Studios.
I hope this helps! Have a fantastic vacation!