3 days in Edinburgh
Edinburgh is a seriously beautiful city with an interesting history, including being the seat of the Scottish renaissance. Arthur's seat is a must for unparalleled views of the city. I highly recommend the Hall of Surgeons Museum if you have an interest in health sciences, it only costs a couple of quid and it's a unique experience. Scottish museum is kinda cool, but pales in comparison to the British museum in London (which I'd unfortunately been to in the past 7 days).
Insider Tip:Free walking tours are good value here. Make sure to grab a haggis, for all that they sound disgusting they are actually delicious. Besides, if you normally eat pies and sausages you're probably eating less-easily-describable parts of animals than go into a good haggis. The peaty whiskeys go nicely with a wee dram of water!