You have a few free dinner options.
- Windjammer buffet. Unlike Cabanas, it does not convert to a sit down restaurant for dinner.
- Assigned/fixed dining. This is the same as on
DCL, with two dining times (I believe it is 6pm and 8:30pm). No rotational dining, so you'll be eating at the same table every night. For a party of 13, it's probably easier to go with this option.
- My Time Dining, aka MTD. You do not have an assigned time, so you can eat when you want. On Oasis, Harmony and Allure, You can book a table ahead of time for up to 10 people, which was a major reason why my family (also a group of 13) switched back from MTD to a fixed time. This probably is something you can arrange once on board the ship, but with a large party, that's leaving quite a bit up to chance.
- Sorrentos pizza. You have to reaaaaaally like Sorrentos (or hate the other options) to go with this. It's not terrible pizza, but it's kind of just there.
For breakfast and lunch:
- Windjammer buffet. Enough said
- MDR. Sit down breakfast, with some buffet options. Custom salads at lunch plus some sit down options
- Wipeout Cafe. Small breakfast buffet, and I believe they make eggs and/or omelettes to order. Burgers, fries and chicken at lunch.
- Park Cafe. Custom salads and various sandwiches at lunch.
- Solarium Bistro. "Healthier" fare.
- Johnny Rockets. Free for breakfast only. Boardwalk is very quiet in the morning, so it's a nice time to eat there.
- Boardwalk dog house. Hot dogs at lunch and in the afternoon.
For food quality of the MDR, it's really dependent on the chefs you get. I've found that the food on Royal and DCL has been at wedding banquet level or better, which tbh is about what I expect. I've liked the food on both (except the two meals I had at Animators, which goes back to my point about the chefs) but it's not been something I'd rave about to my friends as the Best Thing Ever.
I never went to Remy or Palo, so I don't have a direct comparison for specialty dining. But if you choose to pay extra for dining on Royal, I don't think you'll be disappointed. My personal favourite on Allure is Samba Brazilian Grill (Solarium Bistro at night), but I'm partial to the flavours and the flair. There is usually a "First Night Done Right" promotion in the cruise planner where you get half off your specialty meal.
Hope that helps!