If you want someplace nice to eat in Edinburgh then the best there is can be found down in Leith
The Kitchin
It has 1 Michelin* and was best UK restaurant in 2011 and best Scottish restaurant 2012.
It is very expensive but they do a great value set lunch for £26.50 but you must book well in advance.
Another recommendation is
The Withchery up by the castle, it's also expensive but their set lunch is only £15.95
Again early booking is a must
Not so grand as the above is
The Dome which is in a converted bank building. Booking is essential for the main restaurants but you can usually walk into the Club-room Bar and order a meal. You may have to wait in line for a table or you could just stand at the bar and wait for your table while you have a drink.
We now have a new Jamie Oliver restaurant in Rose Street
Jamie's Italian
We've tried twice to get in at lunch time but to no avail - you must book ahead online.
After these I would say try Café Rouge, Bella Italia and then Pizza Express or there's hundreds of others plus all the pubs.
I forgot to mention Harvey Nicols
Forth Floor if you can get a window seat you'll get a great view of Edinburgh.