site has a search engine that will help you identify places that have openings. If you are a little flexible on where and when you should be able to find something. Just go to the "Where to Eat" drop down menu and choose "Make Dining Reservations". You can do the search without making a reservation. The system looks for openings for two hour before and after the time you specify. You can more than one location for a search. For example you can search Animal Kingdom and Animal Kingdom Lodge.
If you have a rough touring plan it might be a good idea to look in the area that you plan to already be in. That should save some time.
In and around the Magic Kingdom, Kona in the Poly, Grand Floridian Cafe in the GF and the Wave in the Contemporary are all good and fairly convenient. Crystal Palace is a buffet that enjoyed in the past but it has been a few trips since I have eaten there. The Plaza may have an opening. It's really a sandwich and ice cream place but the food is good.
Hollywood Studios - Mama Melrose or 50s Prime Time are okay. I think Sci Fi is fun but the atmosphere is better than the food sometimes. Hollywood Brown Derby is good but a bit more expensive.
Animal Kingdom - Tusker House and Yak and Yeti are pretty good. I think Boma and Sanaa at the Animal Kingdom Lodge are better but are not for everyone.
Downtown Disney has a lot of choices but many not on the dining plan. Raglan Road is good and I like House of Blues but it is not on the
DDP. Rain Forest and T-Rex appeals to people with kids.
Good luck