I love the Edinburgh astle; the Palace of Holyroodhouse is worth a look, and the Royal Yacht Britannia. You probably need to book in advance but the "Real Mary King Close" is fun, too
http://www.realmarykingsclose.com/ Can you tell I like doing the history related tourist things?
There are lots of hiking trails up and around Arthur's Seat.
Someone just recently booked seats on the Hairy Coo, a for-tips tour of the country side that looks like a blast
http://www.thehairycoo.com/If you have some money to burn, my BF and I were really impressed with the food at The Atrium
http://www.atriumrestaurant.co.uk/. On the cheaper side, when we were there in February, the Ramada Jarvis hotel on Princes St was doing an afternoon tea for two for £10 - scones, sandwiches, pastries, and of course tea or coffee. The service was fairly lackluster but it was a
lot of good food.
Oh, there's a camera obscura next to the castle! It's a cute gimmick, and would've been better on a brilliantly sunny day, but it includes a whole museum on optical illusions and magic tricks and stuff that was a lot of fun.
http://www.camera-obscura.co.uk/Is this the kind of stuff you're looking for? I love Edinburgh