My favorite solo places are the same as my faves when travelling with a group.
BREAKFAST:
All-Star Resort food courts - excellent food, casual but fun atmosphere, great service.
Electric Umbrella - Pretty good food, best location, great views of either the fountain or the breezeway to MS and TT (hint - sit on the upper level when it's open!)
Starring Rolls Bakery - It don't get no sweeter 'n 'at, hon! Phenomenal baked goods, lovely atmosphere, convenient location.
Kona Cafe - Tonga Toast rocks! And the atmosphere and location are fabu, too.
Boatwrights (POR) - Calm, lazy-river atmosphere, excellent food and service, location convenient if you're staying at POR.
LUNCH:
Electric Umbrella - See breakfast entry above.
Backlot Express - Pretty good food, convenient location, and if you eat during an Indy show, you can sit near the arena and listen to the music and the WHUMP of those cool propane explosions.
Tomorrowland Noodle Station - Best non-burger lunch n MK! Super tasty food, big, bigger, biggest portions for the money, quick service, and great location.
Lotus Blossom Cafe - Excellent Chinese food, large portions, great location. WARNING - No A/C in the dining area make it a hot one in summer!
Tangerine Cafe - Tasty Medeteranian food, nice atmosphere, great location. Sit, eat, relax, and listen to the Moroccan band outside.
Dolphin Fountain - Simple burgers, fries, chicken, sandwiches, etc., but excellent quality, large portions, smiling, happy servers, and a quiet, relaxed atmosphere within the Dolphin hotel. DO NOT MISS the apple pie a la mode - it's terrific!
DINNER:
'Ohana - fabulous food, wonderfuly relaxed atmosphere, great view of MK out the windows. The new menu has turned some people off, but I like it even better, especially the new desert - it totally burries the old pineapple and caramel sauce! Makes a Mickey Bar look like a doggie treat! Makes Dole Whips look like something out of a medicine cabinet! (Can you tell how much I loved that desert?)
Boma - Unusual food, terrific variety, great service, and deserts to die for. Located within AKL, the most beautiful resort in all of WDW.
Yorkshire County Fish Shop - Yes, it's counter service, but I love to grab an excellent fish and chips dinner here and eat while listening to British Invasion. Also a good place to meet folks from the U.K. - they seem to love fish and chips so much that they fly all the way accross the Pond to get it!
All-Star Resort food courts - Excellent counter-service dinner fare, same relaxed but fun-loving atmosphere as the breakfast menu.
SNACKS:
Mickey Bars are great for a quick sweet treat.
Pineapple soft-serve Dole Whips can be a mighty refreshing break on a hot day. Heck, they taste just as good on a cold day.
Kaki-gori is the greatest little frozen treat in Epcot.
I really miss the Beaver Tails at Trapper Bob's, the root beer floats from Pure and Simple in the Wonders of Life, and the Frozun Sundrop from Forty-Thirst Street.