Camera Obscura (actually, I've never been), the Whisky Heritage Centre (ditto), Our Dynamic Earth (the day I went, the rainforest wasn't working), the Botanic Gardens (lovely at this time of year), the former royal yacht Britannia, loads of museums and galleries, the Castle, Holyrood House, the Parliament, Calton Hill, Arthur's Seat, the Zoo (the penguins are excellent), John Knox's house, the Museum of Childhood, Mary King's Close, loads of ghost tours, Harvey Nichols, Valvona & Crolla...
Foodwise, I like La Favorita on Leith Walk, Monster Mash, Suruchi. Dogs on Hanover Street is supposed to be great - I've never eaten there but I used to love David Ramsden's previous place, Rogue.