I think if you have two adults at dinner, a buffet might work well for you. Characters would probably be fun for most 2 yr olds. (Though some seem scared by the characters.)
In a park (using a ticket to enter) ... Crystal Palace at the Magic Kingdom is a buffet Winnie the Pooh characters and nice food. And as mentioned before, the 2 yr old would be free. For non buffets, at Epcot, the World Showcase restaurants are pretty interesting food-wise and quite kid-friendly. We like Chefs de France the best. At Disney Hollywood Studios, 50s Prime Time has a fun atmosphere.
Outside of a park (no ticket required) ... Chef Mickey's at the Contemporary Resort is a buffet with the big 5 characters and good food. 1900 Park Fare at the Grand Floridian is also a great character buffet (particularly if your child is a girl). For non-buffets, Kona Cafe at the Polynesian is a nice atmosphere.
If I have to pick 3, it's Crystal Palace, Chef Mickey's or Kona Cafe.
At Universal, there is some character dining in the parks - ticket is required. There area also some nice restaurants in the resorts (Jake's and the Island Dining room at Royal Pacific, the Kitchen at Hard Rock, and Mama Dellas at Portofino Bay.) And there's dining at City Walk, which is kind of like Downtown Disney (no ticket). However, you really don't need to make reservations more than a day in advance for most places, so you'd be able to scope out the restuarants when you get there or talk to the concierge. Also, like at Disney, some of the counter service are very well themed (like in the Dr. Suess area). The food is better at Disney counter service in my opinion, but I think you'd do just fine in either place.