This sounds very childish & I know there has been a lot of bickering on the thread about a direct GLA
to Germany flight, however.....
Simply go to Glasgow! It is only 70 km away.
However, I agree that there's plenty to do in Edinburgh for 2 days.
If the weather's good, try and get a window seat on the right as the normal approach over the estuary will yield fantastic views of the Forth Rail Bridge. In fact taking a train over the bridge would also be a good idea. Buy tickets for North Queensferry (just over the bridge) or Inverkeithing which will have more trains stopping.