You say that your first two night are booked. I'm assuming that is in the Glasgow area. There are many wonderful museums and galleries in Glasgow, most of which are free. A lot will depend on how tired you are after your trans-Atlantic flight as to how much you want to see on May 24th.
If your last three nights are in Edinburgh, that leaves you with nine days/nights on the trot.
Personally, I would skip Oban. I like Oban, and I love Mull and Kerrera, but that is going to tie up two days, and you don't have that much time for your "sampler" visit.
Here's what I would recommend for your time in Scotland:
Day 3: Take the A82 along the shores of Loch Lomond. Have a brief stop in the village of Luss on the west shore. Continue through Glencoe on the A82. Take a couple of short hikes if the weather is conducive. Stay on the A82 to Fort William, and stay there. If you get there early enough, take a drive up Glen Nevis, or take the Aonach Mor gondola, if it's running.
Day 4: Take the A830 to Mallaig. Check out the Glenfinnan Viaduct, especially if the Jacobite is running. Once in Mallaig, take the ferry to Skye (reservation essential). If you can't find accommodation on Skye, do a day loop: A87 to Sligachan, A863 to Struan, B885 cross-island road to Portree, A87 back to the Skye Bridge. Stay somewhere near Kyle of Lochalsh. Actually, now that I think about this, it would be more scenic to take the A87 to Portree, then head for the bridge via Struan and Sligachan.
Day 5: Visit Eilean Donan castle. Double back and take the A890 to Strathcarron, then the A896 to Lochcarron and through Glen Torridon to Kinlochewe. For a real adventure, take the Bealach-na-ba hill pass to Applecross, then follow the coast road around the Applecross peninsula to Shieldaig. From Kinlochewe, follow the A832/A835/A9 to Inverness. Stay overnight in Inverness.
Day 6: Explore the Loch Ness area. You could visit Culloden Moor, as many visitors do, take the Ness Islands walk, do part of the Glen Affric walk, and possibly catch some some music in one of the venues in town. Stay overnight in Inverness.
Day 7: A96 to Nairn, then the A939 through Grantown-on-Spey to Ballater. A quick visit to the outside of Balmoral Castle, then the A93 east to Crathes Castle. From Crathes, the A957 Slug Road to Stonehaven. If it's not too late in the day, visit Dunnottar Castle. Stay near Stonehaven.
Day 8: Two choices: You can visit Dunnottar if you didn't have time to do so the previous day, then either a) Take the coast road (A92) to Dundee, stopping in Montrose and Arbroath along the way, and visiting the spectacular Lunan Bay and the Arbroath cliff walk; or b) take the fast road (A90) to Dundee, then cross the Tay Bridge and visit St Andrews and the towns along the East Neuk of Fife. Stay in Dundee or somewhere on the East Neuk.
Day9: Continue to explore the East Neuk/St. Andrews/Dundee area. Overnight near Dundee.
Day 10: Take the A90 to the M90 to the A9 and visit Stirling. Visit the castle, the Wallace Monument, and Doune Castle.
Day 11: Head for Falkirk and visit the Wheel and the Kelpies. If you're Outlander fans, visit Blackness and Midhope Castles on the way to Edinburgh.
This is starting to sound like If It's Tuesday, This Must Be Belgium! (I'm showing my age!) However, this is just a general outline of what I would try to accomplish if I had the number of days which you have. All of this is subject to modification, and it certainly puts paid to your striving to spend at least two nights in each place.
Best wishes for your plans! I can 100% guarantee that this will not be your only trip to Scotland!
p.s.: Just south of Stonehaven is the amazing Fowlsheugh Nature Reserve, where a short walk will bring you to steep sea cliffs which are home to thousands of gulls, guillemots, razorbills, kittiwakes, and even puffins.