I'm relatively new to Edinburgh but already the staff in Pancho Villa's on the Royal Mile recognise me as that is where I go with my children when they visit. They are in their 20's and like Mexican food. You can go in a crowd and wear sombreros (if you would like to.....)
The other place I have been a couple of times and would recommend is David Bann's which is on St Mary's Street ( I think). It is a vegetarian restaurant. My daughter who is vegetarian took me there and we go on special occasions. Last night when we passed ( after coming out of PV!!) it was full - on a Tuesday night - so that is always a good sign.
And finally I also like Amarone which is on George Street. I've never had a bad meal there.
Oh I forgot, I am going for Champagne afternoon tea to the Peacock Inn down in Newhaven next week. Haven't been before, but have been told that it is good. When I went in to book there was the most wonderful smell and also it was busy too.