Seems to be for locals and tourists.
No 1 HIgh St, of that address on the Royal Mile and despite the address just off the very touristy end of town. Reliable food, pub-style but seems freshly and locally done. Haggis tower looks and tastes great.
Sandy's Bar Forrest Road, nr. George IV Bridge and Greyfriars. Quickly crowded but an authentic feel and certainly the place for live acoustic and Scottish traditional music. Traditional beers too.
Cafe No. 33 Stockbridge. Take a walk along the Leith and stop here for really good coffee and paninis, sounds hipsterish but isn't, just decent modern food and OK prices.
Clarinda's. This is a must if you want an olf-fashioned tea-room theme with breakfast, lunch and tea and cake menus with friendly service. Towards the Holyrood end of the Royal Mile and worth the walk if you're at the other end of town.