Here's what I would do. I'm assuming an evening arrival on Day 1 and travel by rental car. With so few nights, there are going to be 1-night stays, which aren't ideal but it's the only way you will see a lot of the country because it is spread out and the roads don't make for very speedy travel. I'm also giving the cities short shrift, which may not be to your liking, but here goes.
Day 1: arrive Glasgow, stay at an airport hotel (the Holiday Inn is great, the Holiday Inn Express acceptable),
Day 2: get rental car in the morning. Be sure to ask the rental car agent which signs to follow at the roundabouts leaving the airport campus to get on the Motorway headed toward Loch Lomond (they are not self-explanatory, IMO). Drive north over the Erskine Bridge, through Dumbarton, along Loch Lomond and stop in Luss to take a short cruise on Loch Lomond. Proceed over the passes to Inveraray and stay 2 nights at Brambles.
Day 3: see Inverary Castle and Auchindrain Township open-air museum, also sights in the town of Inveraray.
Day 4: drive to the Isle of Skye (or Dornie, near Kyle of Lochalsh bridge) by way of Fort William. You can go via Glencoe or via the Connel bridge; each of these routes has its good points. Near Fort William, stop to see Old Inverlochy Castle and turn off briefly for Banavie to see Neptune's Staircase.
Day 5: see Isle of Skye, for example Dunvegan Castle and/or a hike.
Day 6: drive to Pitlochry or thereabouts. You'll have to decide whether to see Culloden Battlefield or take a hike in the Cairngorms or tour Dalwhinnie distillery.
Day 7: drive to Edinburgh, turn in rental car, stay at an airport hotel.
