By no means an exhaustive list, but these tend to have good to excellent availability for dinner the day of. As mentioned, it's best to check the app and make a reservation even if it's only 5 minutes ahead.
Turf Club - Saratoga Springs
Olivia's - Old Key West
Boatwrights - PO Riverside
The Wave - Contemporary
Grand Floridian Cafe - Grand Floridian
Maya Grill - Coronado Springs
Trail's End - Fort Wilderness Campground
Garden Grove - Swan
There are lots of others that likely have availability on any given day, including
Artist Point - Wilderness Lodge
Jiko - Animal Kingdom Lodge
Boathouse - Disney Springs
Homecomin' - Disney Springs
Raglan Road - Disney Springs
House of Blues - Disney Springs
Whispering Canyon - Wilderness Lodge
Note: all of the above appear on the app as having availability for dinner around 7pm, today, Labor Day, 2017, along with a whole lot more.
Steve