The main reason to head to Skye (although not the sole reason) in my opinion is for the Cuillin mountains, especially the Black Cuillin which represents the best Alpine style climbing in the UK. It's rough and tough and not for the inexperienced or casual hiker. There are other attractions like the Trotternish ridge and the fact that it's big and empty away from the tourist hot spots like the Fairy Pools, Portree etc.
Might I suggest Aran as an alternative? Mountainous in its northern part, a couple of attractive towns, Neolithic sites on the west side in particular, remote beaches. Not for nothing is it called 'Scotland in miniature'. And it's easily reached from Glasgow (about an hour's drive to Ardrossan where the CalMac ferries depart for Arran).
Downside would be trying not to clash with 'Glasgow on holiday' when it's relative proximity makes it busy.
The Shetlands are hard to reach and in my recollection very empty. Nothing wrong with that if you like big and empty! I always tell people that my interest in birds sprang from there as there was nothing much else to do, particularly outside Lerwick! There are quite a few sites to investigate and you'd probably not be mobbed with tourists, but I wouldn't miss the mainland Highlands if you haven't been there already. My main recollection of Shetland was walking across the Hermaness bird reserve to view the Muckle Flugga lighthouse (and to try and see the resident albatross, several thousand miles off course. It will, however, be long gone by now - it was a long while back) all the while fending off attacks from the resident Arctic Skuas (Bonxies) which dive bomb you as you walk the not inconsiderable distance across the reserve! An unopened umbrella proved handy - holding it above your head meant they attacked that and not your actual head!
It's a thought anyway! Have a great trip wherever you end up!