I echo the suggestion to do the Big Thunder Ranch BBQ, as it is supposedly closing after January 10th.
I agree that Blue Bayou is the most iconic restaurant at DL, and it's unique to DL, so it's worth trying. It's not my personal favorite, but many people love it.
As for table service restaurants, I like Carnation Café in Disneyland, Wine Country Trattoria in California Adventure and Storytellers Café in the Grand Californian Hotel.
As for counter service places, you can't go wrong with Plaza Inn in Disneyland. I also like Tangaroa Terrace at the Disneyland Hotel.
My favorite character meal is Goofy's Kitchen at the Disneyland Hotel, but many people prefer Surf's Up with Mickey at the Paradise Pier Hotel.
In Downtown Disney, people love Ralph Brennan's Jazz Kitchen (which also has an Express window for takeout). There's an ESPN Zone there, a Rainforest Café, La Brea Bakery, Catal, Tortilla Jo's, Naples, etc.