In Magic Kingdom:
Counter Service is the most prevalent.
Casey's Corner
Pecos Bills
Columbia Harbour House
Pinnochio's Village Haus
(Too name a few - there are a few more in Tomorrowland)
Table Service:
TOny's Town Square
The Plaza
Crystal Palace (Characters)
Liberty Tree Tavern (Characters at dinner/none at lunch)
Cinderella's Royal Table (Characters at breakfast and lunch/none at dinner)
Resorts nearby:
Contemporary
Cali Grll - dinner only $$$$
Concourse Steakhouse - lunch/dinner
Chef Mickey's - breakfast/dinner (Characters)
Polynesian
'Ohana - character breakfast/dinner (no characters)
Kona Cafe - b/l/d (no characters)
Grand Floridian
GF Cafe b/l/d
1900 Park Fare - breakfast/dinner both with characters
Citricos - dinner $$$$
Narcoosee's - dinner $$$
Victoria and Albert's - dinner $$$$$
Hope this helps.
You can also boat to the Wilderness Lodge for:
Whispering Canyon Cafe - b/l/d
Artist Point - dinner $$$$