Hi Mike, well, you're making my head spin! 😊 Just for clarification, it looks like you've got about 15 nights to spend. Is that correct? That would give you about 14 days.
The others are all correct. Your schedule is so fast, and you will spend almost all your time on the road and not get to see hardly anything at your final destinations. So if it were me, I would remove Thurso, Orkney and Shetland from your list and save them for another trip. I'm assuming this is your first trip to Scotland, but I can guarantee you will want to come back.
If you're flying into Edinburgh, I would give three nights to that city. Two nights will only give you one full day, and there's a lot to see there. And then you've got one night in Glasgow, which is doable. If you leave early from Edinburgh on your third day, you would have the rest of the day and then part of the next day, I'm assuming. After that, is when you want to rent your car.
After Mull, you could take the ferry from Tobermory to Kilchoan, then drive to Mallaig, take the ferry to Armadale then drive up to Portree. I would spend a minimum of three nights on Sky, and four would be better. After Skye, you could head to Inverness and use that as a base for two nights. Besides the two items you mentioned, you could also visit Culloden and Clava Cairns, which are standing stones that are quite unique.
At this point, you've got:
- 3 nights in Edinburgh
- 1 night in Glasgow
- 3 nights on Mull
- 4 nights on the Isle of Skye
- 2 nights in Inverness
That's 13 nights. From Inverness, you could begin your drive back to Edinburgh a number of ways. The first would be to head south through the Cairngorms, which would give you some lovely scenery to see there. You could overnight in Pitlochry along the way.
The second would be to head south again, but this time deviate a little bit to the west and drive down through Loch Lomond and Trossachs National Park. One advantage to doing this is that you could change your plan a bit and instead of stopping in Glasgow in the beginning, you could head to Glasgow after Loch Lomond and spend a night or two there.
The third option would be to head to Edinburgh via the northeast coast, which would take you from Inverness northeast then along the coast through Nairn, Portknockie, and further down the east coast. You could stop at the Bullers of Buchan, which are amazing, then make your way down to Cruden Bay and visit the ruins at Slains Castle. And then head down to Edinburgh from there, spending the night at whatever place along the coast takes your fancy.
Obviously, this is your trip, and you are entitled to do it the way you want. But all of us are experienced travelers, and we have all been to Scotland and spent time there. We know how tempting it is to see everything, but the problem is that the roads are mostly single track, especially in the Highlands, so you won't be going very fast along them. And even on the mainland, it's slow going.
NOTE: I just noticed you said you will be there from mid-June through mid-July. So are you planning to be there for a month? Because that's not what your itinerary looks like. That would be helpful to know. If you're going to be there for a month, then could potentially throw in Orkney and/or Shetland.
The more details you give us about your trip, the more we can help you work out an itinerary that fits your needs.