How large is your party and what places have availability? Do you want something special? Something traditional? Great food or atmosphere? Is price a factor in that a signature restaurant would be out of budget?
Without knowing that, there's only so much advice that can be given.
That being said, I've found that when park restaurants are full, resorts are a very good and overlooked alternative.
Case in point, last year, we (my extended family) were staying at POR and decided to go to Boatwrights for an early (5:30ish) dinner before heading to
MNSSHP. We made the reservation at the last minute. We weren't particularly tempted to try Boatwrights before simply because the lot of us have been to or lived in Louisiana long enough to wonder if food there was going to be up to par. But, because we were staying onsite and because we wanted an easy option for dinner, reservations were made. The meal was
incredible, with even traditional cajun dishes like étouffée getting very good marks from our group. And the restaurant was pretty empty.
I've read great reviews from other mod sit down restaurants, but have only been to Boatwrights.
Signature and buffet restaurants at deluxe resorts are great as well. A few years ago, during a Poly stay, we only ate CS at Poly but hit sit down restaurants at every other hotel around the lake

. Citricos was great, and Artist Point was very special (got lots of pixie dust there). Both tend to not sell out (during my personal holidays...I don't know how they'll be on Thanksgiving). Last year, we went to Cape May on our last night and everyone left stuffed and happy.
And if those types of restaurants were sold out and I were going with my family...I'd pick a resort I hadn't been to and visit their food court. Over the past several years, my family has gone to a 'new' resort for breakfast at the food court in order to scope out the resort for a future stay. Have visited Grand Floridian, CSR, and WL that way. So, you could pick a resort with a food court and have lunch or dinner...and tour the resort...walk around, check out the pool, gift shop, etc.
Finally, something at Disney Springs should be open. Raglan Road is great if you can get reservations. We spent Christmas Day there years ago, when it was DTD, and had a great time shopping and eating counter service.
Just be flexible and remember that it's Disney. As my son said the other day, "it doesn't matter where you stay at Disney, you know it will be great."
Good luck!