Don't attempt a last-minute trip during the Festival (August), unless you love searching for private accommodation on craigslist and message boards.  If you ignore this advice then...

Don't book a bed through Scottish Ski Holidays.  After sending in money and signing a contract they informed us the room we booked was not available after all.  For the replacement room, they gave us the wrong phone number and owner name, so we could not contact her in advance to make sure she would be there to let us in to her house when we arrived.

Don't forget a coat.  Even in August it was pretty chilly and windy.  

Do check out the paintings at the National Gallery of Scotland.

Do catch a cheap and filling breakfast at Snax.  Follow the signs to the cafe from Princes Street just East of Waverley Station.  

Do burn off the calories from said breakfast by climbing Arthur's Seat and Calton Hill.  Both have great views of the city, and Calton Hall has a number of 19th Century monuments.  

Do get to Edinburgh Castle early in the morning before the crowds get bad.  Skip the audio guide and join one of the free guided tours.  

Do eat at Amber, the restaurant at the Scotch Whisky Experience on the Royal Mile.  A bit posh looking, but surprisingly affordable food for that part of town, and very, very tasty.  Eat at lunchtime, the prices really jump up for dinner.  

Do take a ghost tour.  Ghost Hunter Trail comes highly recommended.