I'd visit Edinburgh Castle, then walk down the Royal Mile to Holyrood Palace.
As someone suggested, buy your tickets ahead of time online.
As you walk down the Royal Mile, you can pop into some of the closes, enjoy a pint in one of the many pubs (World's End is a favorite!) or stop for lunch at one of sidewalk cafes. There are lots of shops selling souvenirs, woolen scarves, kilts, etc.
That would make for a nice visit!