There are all kinds of Thanksgiving meal options around Disney. We did the buffet at Storyteller's Cafe at the GCH the last two years, and it was a great experience. I felt the price was reasonable for what you got. There was also an order off the menu option, but since it was Thanksgiving, we preferred the idea of the buffet. There were salad choices, fruits, a couple soups, several meat choices including turkey, several Thanksgiving-type sides (some traditional, some a little more creative), and a lot of tasty mini desserts. They deliver a bread basket to your table, unlimited non-alcoholic drinks (you can order alcohol at extra cost), and there was even fresh scooped ice cream if you knew to ask. This meal was completely booked before Thanksgiving day though, so it's something you need to call ahead and make a PS for. When I called last year, the CM I spoke with mentioned that the PCH Grill at Paradise Pier was also offering a special Thanksgiving menu and Goofy's Kitchen would have seasonal choices as well plus the usual characters.
I know some of the DtD restaurants offer Thanksgiving meals; someone on here really enjoyed The Jazz Kitchen. Mimi's, a chain restaurant not on property, located near the Hojo hotel on Harbor serves a special Thanksgiving meal.
Inside the parks, a few of the restaurants will offer turkey and fixings on the menu for the day. I can't recall which places for sure, but I think Plaza Inn and Carnation Cafe are two of the places in
Disneyland that will do this.