The Museum is open until 5pm, that will kill an hour and has the best view in town from the roof terrace.
Loads of nice coffee places – hangout and people watch at the Elephant House (where JK Rowling DIDN'T write Harry Potter, that was the place that was closed for years and has recently re-opened as Spoons).
Wander up to the Castle esplanade, check out some of the cool old pubs off the High St, wander down to the New Town and observe the Yahs braying in their natural environment.
Or, 4-9pm ? Thats time for a circuit on the 52/32 bus – see how most of the world lives in Edinburgh. Irvine Welsh reckoned that should be compulsory for all tourists.