(Lowland) Walk the Royal Mile from the Castle to Holyrood House in Edinburgh, see the little alleyways where Burke and Hare performed their evil deeds. Be there for the one o'clock gun. Join a "ghost walk".
(Lowland) Visit Loch Lomond, beautiful and quite near to Glasgow. (Don't worry too much about visiting Glasgow, a huge faded industrial conurbation, the people are nice but the town isn't particularly noteworthy.)
(Highland) Go to the Visitor Centre at Loch Ness (and be a bit disappointed when they debunk the legend). Try to do this on a bright, sunny day, the Great Glen is a gloomy place otherwise.
(Highland) Visit Glencoe - scene of the Macdonald massacre - do this on a gloomy day, it adds to the atmosphere of the place.
(Highland) Visit Culloden, the battlefield is well laid out with an excellent visitor centre - notice how there were Scots fighting for both sides.
(Highland) Watch ospreys fishing in Loch Garten. Watch eagles soaring over the western highlands.
Don't bother with Ben Nevis - it might be tall but it's boring and you can't really see the whole mountain from anywhere sensible.
(Highland) If you are brave, take a car and drive the Bealach nam bo (pass of the cattle), the steepest navigable road in Great Britain, the views are stunning, and you'll end up at Applecross, once supposed to be the most remote village** on mainland Britain. (There's a new road now, much less fun.)
https://www.visitscotland.com/wsimgs/applecross_1840734929.jpg
** That title now goes to Inverie, on the Knoydart.
(Highland) Look out for Corrieshalloch Gorge, spectacular!
There is a mix of lowland and highland places here, and Scotland is larger than you might think. To see all the above, and do them justice, you'd need three weeks, and you'd be travelling quite a lot (and remember there are few good roads in the highlands).
