In case you are not aware, the UK makes wide use of speed cameras, and they also use something called "average speed check," most often in motorway work zones. "Average speed check" is designed to combat the well-known habit of motorists slowing to pass a speed camera and then speeding back up. The system uses two or three cameras spaced some distance apart, all of which read your number plate. The system then calculates how long it took you to pass the cameras. Because they know the distance between cameras and the speed limit, they can determine whether you were speeding.
If you have not previously driven a right-hand-drive car, it's not a bad idea to try to drive on the airport roads a little bit before heading to the motorway. Bear in mind the bulk of the car is on the opposite side than you're used to, so you will be positioned much further to the right in the lane, and bear in mind the rearview mirror is to your left. I found driving on the left easy enough after the first few miles, but the rearview being on the left required overcoming years of muscle memory and parking in indoor car parks with pillars and such was a little tricky. Operating the manual gearbox with my left hand was a non-issue, no difficulty at all.
USE YOUR BLINKERS at roundabouts. This includes indicating a right turn if you're going more than halfway around, then indicating left when you're going to exit. The right indicator tells people waiting to enter that you will remain on the roundabout and they need to give way to you. The left indicator tells them you're exiting.
Currency tip: Note that Scottish pound notes are issued by a number of banks in Scotland and may or may not be accepted in England. Bank of England notes will be universally accepted. If you have more than a small amount of Scottish pound notes when you're preparing to head back south from Edinburgh, it might not be a bad idea to stop at a bank and ask to exchange them for Bank of England notes. I was once at dinner with a group of friends near Bristol and they all put down cash towards the bill. Then I realized since my American Express card gave me miles based on the dollar value, it made more sense for me to charge the whole bill, so I picked up all the cash and charged it. Some of the people I was with were from Scotland and had put down Scottish banknotes. When I tried to use one of those the next day at the Clifton Suspension Bridge gift shop, the shopkeeper wouldn't take it (good thing I had plenty of Bank of England notes). The currency exchange at Heathrow will take the Scottish notes if you still have them at the end of your trip.
With that said....
If you like Scotch whisky, obviously there are lots of distilleries. If you go to John O' Groats, you'll pass right by the Glenmorangie distillery in Tain. That might be the most convenient one to visit. There is also a good whisky shop at Heathrow, Whiskies of the World.
If you're into golf, make the pilgrimage to St. Andrews. It's not too far out of the way on the drive from Aberdeen to Edinburgh.
The Museum of Flight in East Fortune is an interesting stop and you can tour the interior of Concorde G-BOAA.