Ooh I missed the splurge restaurant. We had a wonderful meal at The Gardener's Cottage a couple of years ago and really enjoyed it. It has several communal tables. It was lovely.
Several years ago we went to Stac Polly. They serve Scottish food and it was wonderful too.
If you like seafood, consider Fishers. There are a couple of places. I don't think that they will have Arbroath Smokies while you are there as they don't have them during the festival-or at least they didn't used to--but the seafood of Scotland is wonderful. You can branch out from Salmon.
I also like The Mussel Inn in New Town. I've usually had lunch there but dinner is likely very nice.
We found The Gardner's Cottage when I looked for new restaurants and decided to try a new place. You might also want to explore what is new. Here's an article from December. Here's another article to check out.
And I have to share what also came up from my search! The best "American" restaurants in Edinburgh!
Lots of good eats in Edinburgh.