First that comes to mind is Edinburg castle. There are free volunteer guides that conduct tours around the castle grounds as well as it's interior and explain who, what why and when it was built etc. If you are there during the annual military tattoo, buy a ticket and make sure you do not miss the pageantry and spectacle of fine military marches, music and the melodious bagpipes. Various Scottish dances and spectator sports mat be staged too. You will enjoy it for sure.
Do not miss all the lochs in Scotland, they are simply breathtaking and scenic. Two must see are Loch Lamond and Loch Ness and you may, just may catch a glimpse of Nessie if you are extremely lucky.
Aberdeen is a picturesque little town with a spectacular seaside and King's College where you can take in the old scottish air.
Another highly recommended destination will be the Isle of Skye, a beautiful little island North of Scotland, very romantic and peaceful.
Of course, do not miss Ben Nevis, Scotland's highest mountain.. There are stone circles that smaller but similar to England's Stonehenge.
Attend some Scottish dances, the cultural kind. It is a must see to get a feel of Scottish history. Look out for Scottish swords, kilts and bagpipes for sale, they make for interesting souvenirs of your trip to scotland.
Try their Scottish haggis, a favorite meal in the country consisting a sheep offal encased in sheep intestine. Very unique and only available nowhere else.
There are underground mines that visitors can experience and buy their semi-precious stones costing a pound each that you can collect as souvenirs for friends or keep as mementos. they come in various colors, some touquoise, some aquamarine, some ruby red, others purple, green, pink, orange and also shiny black and translucent.
There is also a "Dinosaur Park", where life-sized replica of various extinct dinosaurs are displayed for all to see and admire. Look out for a replica of the Scottish Loch Ness too.
There is a seaside bay with the long name that starts with A. A cable car runs up the hill for a view of the surroundings. http://en.wikipedia.org/wi
Will suggest more if you require further recommendations. about 5 years ago
Gregorian chant by Benedictine monks at some old churches are concerts you should not miss. It is spiritually uplifting, no matter what domination your religion may be.
Do look out for their highland "coo", or cow with unbelievably long fur, very reminiscent of the Tibetan yaks. The highland coo are very tame and docile and you can go right up to them to stroke them. about 5 years ago