Royal Yacht Britannia at Ocean Terminal (get a bus).
Train to Dalmeny (= South Queensferry station) and go and look at the Bridges (pleasant place to get food, South Queensferry, too).
Marvel at the mess that has been made by the tram works...
Good point, minotier, I'd forgotten the galleries.
User1314, I think I've been in the Haymarket bar exactly once... if you're still in Edinburgh, go left out of the Haymarket Bar, stay on that side of the road, there are several restaurants on that stretch, the Chinese one there does a different kind of Chinese food, it is very good. I enjoyed the sushi I had at Hay Sushi too (I don't know much about sushi so I have no idea if it is good sushi or not, but I liked it...)