The roof of the museum of scotland is great for some stunning views over Edinburgh, as is a wee walk up Calton Hill, of course.
L'escargot Bleu as mentioned above sounds great - and L'Ptite Folie on Queensferry Street is a fairly cheap French restaurant with really lovely food in a (I think) charming little place.
Avoid the Royal Mile unless you like tat.
The Elephant House and Always Sunday (OK, it's on the Royal Mile so I just contradicted myself) are two really nice cafes in the city centre and do good cake!
Oh, and the Gallery of Modern Art (which has the best cafe in terms of food in Edinburgh, I think) and the Dean Gallery, both off the Water of Leith in the west side are both highly interesting and worth a look out if you're in the area.
