i enjoyed walking the seaside on the promenade at portobello while staying in edinburgh 2 yrs ago, but can't remember if i ate anything or not while there. it probably would have been fish and chips, in the spirit.
i went on a ghost walk one evening--you should be able to get a city bus there and back--as well as the santander-sponsored walk (1.5 hrs, daytime, pay what you think it's worth). the tourism office could have more info. i know those walks are very very touristy, but they were a very nice way to get oriented, i saw lots of little corners i would haven't have thought to check out. and the ghost walk ended with a free drink at a pub--where i ended up at a table with people from my own province, which is almost unheard of.
at edinburgh castle, i was trapped in the gift shop as charles and camilla drove past, which i wouldn't repeat but it was somethign interesting to write home about.
a very very very touristy thing i did was the sort of 'underground city' attraction at mary king close, from the same people who do other historical attractions like Canterbury Tales. but again, it was an insight into part of edinburgh's history and i didn't see any other way of discovering it. it was rather kitsch but still fun.
the elephant cafe (j k rowlings) was another surprise; again, it's on everyone's radar, but it really is just a local cafe full of people going about their day. it had a nice feel, good coffee, good food.
i did see one pub that seemed to have a party with scottish dancing going on--real people, not dancers. but i was still suffering after effects of a 48 hr indigestion attack, so i didn't go in.
mostly i tried to drink a lot of scotch.