The Museum of Scotland is worth half a day of your time. Fantastic buildings if you like architecture, and some of the displays aren’t bad either. Make sure you go up to the roof terrace if it’s open.
The Camera Obscura is pretty cool, if only for the view, but best on a clear day for reasons that will become apparent if you go !
If the weather is good a walk up Arthur’s Seat, then wander over to Duddingston for a pint in the Sheeps Heid, oldest pub ever in the entire history of human drinking (or so they say).
Or if you prefer to keep it real you can get all Irvine Welsh on it, who famously said that all tourists should do one trip on the 52/32 circle bus for a tour of the less groomed suburbs.
Get a train from Waverley out to South Queensferry and look at the Rail Bridge, Hopetoun House is quite good too while you are out that way.
