Hi Christine,
Thank you for visiting us at the Disney Parks Moms Panel! I'd get a jump start on booking an
Advanced Dining Reservation, as Thanksgiving is a very popular evening to have dinner plans set. On quick glance for a table of 4, there are very few tables available at this time. If you'd prefer a served meal as opposed to a buffet, I'd suggest watching for cancellations at Liberty Tree Tavern, known to serve traditional family-style Thanksgiving fare or
Artist Point at Disney's Wilderness Lodge. Feel free to click on the above Advanced Dining Reservation link to view the current availability for tables of 4. The description will indicate whether or not the meal is table served or buffet. As Thanksgiving approaches, you might be lucky to snag a last minute reservation as guests' itineraries change and I'd also suggest giving Disney Dining a call to see if they might be aware of special Thanksgiving meals offered at specific locations. You can contact them at 407-WDW-DINE.
If you don't mind leaving the Parks, typically Downtown Disney will offer more availability and the restaurant options are really great. The above link showed Portobello and Paradiso 37 both having availability that evening, which I'd highly recommend for expansive menus, quality and ambience. I've also heard Raglan Road was offering a Thanksgiving meal, but availability might be challenging.
I wish you a magical vacation, Christine, and please feel free to visit me again with further planning questions.
Best wishes,
Sherri