Another suggestion for Dunnottar Castle - my wife and I were in Aberdeen just a couple of months ago and Dunnottar was the highlight of a really incredible trip. Try to go at about 10 or 11am on a bright, sunny, warm day - the warm land will pull a really dramatic mist in off the sea and make the castle seem to lurk in the mist - very spooky and a lovely effect. Don’t be intimidated by all the stairsteps down to the beach and back up to the castle - you’ll be more than rewarded for your hike.
The nearby village of Stonehaven is really nice, too - a great place to spend an afternoon and get a bite to eat.
If you get half a chance, GO INTO THE HIGHLANDS. The roadside scenery alone will reward you.
See if you can get a tour of Marischal College (now part of the University of Aberdeen) - the architecture is spectacular and the museums are very impressive.
Cullodden Battlefield is only an hour or two from Aberdeen (toward Inverness) - worth seeing if you’re interested in Scottish history.
The Speyside whisky distilleries are also between Aberdeen and Inverness, and most of them have tours available (usually including a sample of one of their products…)
If you get up near Loch Ness, definitely check out Urquhart Castle. Sure, it’s usually crowded with tourists (it is one of the most famous castles in the counrty) but it’s also breathtaking. And the Loch is beautiful. Do the boat tour - we missed out on that.
Depending on how busy your time in Aberdeen is, you might have time to go all over Scotland by car or bus. If you get a chance to take a (relatively) long drive, Glencoe is the most beautiful place in the world. In the same general area, Loch Lomond is lovely, as well.
Take plenty of film. And have fun. And remember, you MUST go to Dunnottar. Many locals don’t even know about it somehow, so the father-in-law might get a thrill, too.
Feel free to check out our trip here and here. Some of the places we went require special arrangements to visit (Inverugie Castle and Keith Hall in particular…) but you might get some ideas for your visit.