Scotland "must sees" depend on what tickles your fancy.
The usual tourist trail will consist of visiting Edinburgh Castle, a tartan shop, Loch Nessie, a tartan shop, tour of a Speyside whisky distillery, a tartan shop, Skye and yet another tartan shop. All very touristy and predictable but it's what the average tourist seems to want.

May I suggest some alternatives?

Stirling Castle....in my opinion the best touristy castle in Scotland with a magnificent braveheart view of the battlefields below. The town isn't that great but further up the road the fair city of Perth is a lovely Scottish town.
Loch Tay.....no monster but more scenic and interesting than Loch Ness with some nice hostelries along it's shores.
Glasgow.....not the capital but has far less tartan shops to catch out the weary tourist.
Try the Island of Mull instead of Skye....at least you still have to take a ferry to get there. Oban isn't a bad wee town to spend an hour or two in while waiting for the ferry.....just keep one eye on the seagulls there though. They have a habit of stealing your fish supper when you're looking the other way.

No idea about Ireland I'm afraid....I've only been to Dublin and didn't think much of the place to be honest.