Edinburgh Castle (entrance fee about £21 now).
National Museum of Scotland in Chambers Street is free to enter. One end is devoted to Scottish history, you start in the basement (oldest stuff) and work up the levels to the present day. They have a decent but pricey restaurant for lunch in another basement at the other end (ask), and two other cafes on the floors above. Special exhibitions may charge a fee.
Mary King's Close tour Home - Real Mary Kings Close
Finish off with a walk around the Botanical Gardens (27 bus from the Mound).
More art galleries than you can shake a stick at if you are into it. Personally, never been. National Museum of Scotland comes highly recommended.
If the weather is half decent, I recommend a walk up Arthur's seat for a view. If you can't be arsed, you can get a decent view of the Forth from the cafe in Harvey Nicks.
Don't forget a stadium tour of Murrayfield. You might even get a glimpse of the Calcutta Cup....
I don't know if they have started up yet, but a boat trip out of South Queensferry round the Isle of May, under the bridges, and up towards Crombie comes highly recommended from my Wife, though I suspect that in her case it was Prossecco fueled. The QE is at Rosyth, so you should be able to see it from the water.
I used to live in the castle, if you really want to impress folk ,have a word with the guard and when the castle is closed for the day but there are still a load of tourists in the area march boldly up to the drawbridge, raise both arms in the air and shout "Open Sesame" then march through the now wide open main gates. Always used to get gasps of amazement when I did it. Its even more impressive if its dark and they put the spotlights on inside for you.
1)Light-on-Loafers mincing around outside pubs.
Fhaaasands of 'em.
2) Any shop selling tartan anything. Cnuts. All made in Taiwan.
3) Beggars. EG... most of the population.
4) Over priced micro-meal serving rip-off eateries.
6) Used condoms are slippy...allegedly.
7) Dock-end of Leith Walk. Full of hookers. Then again.....
Princes St. Full of hookers waiting for their shift in Leith Walk.
9) Anyone with an Edinburgh "accent". There is none...they just think there is.
10) Mind the trams . Stupid drivers won't swerve for you.