Ok, great.
The immediate area around Oban doesn't have many really unmissable walks, but Beinn Lora
https://www.walkhighlands.co.uk/argyll/beinn-lora.shtml is a good viewpoint, and Seil Island is worth a visit for
https://www.walkhighlands.co.uk/argyll/ellenabeich.shtml and/or
https://www.walkhighlands.co.uk/argyll/cuan-seil.shtmlHowever, it's not far to the Glen Coe / Fort William area which is more dramatic with a couple of low-level classics - the Lost Valley
https://www.walkhighlands.co.uk/fortwilliam/lostvalley.shtml and Steall Gorge
https://www.walkhighlands.co.uk/fortwilliam/steallfalls.shtml There is plenty to do on Skye but I would recommend Beinn Tianavaig
https://www.walkhighlands.co.uk/skye/bentianavaig.shtml as a beautiful small hill and Coire Lagan
https://www.walkhighlands.co.uk/skye/coirelagan.shtml to get close up to the impressive Black Cuillin hills without any serious difficulty. The Old Man of Storr
https://www.walkhighlands.co.uk/skye/old-man-of-storr.shtml and the Quiraing
https://www.walkhighlands.co.uk/skye/quiraing.shtml are very spectacular but also get very busy - try going either early or late in the day (there will be plenty of daylight in June!)to avoid the worst of the crowds.
Again the immediate area around Inverness is not so special, so it is worth travelling a bit. You can go south to the Cairngorms for Loch an Eilein
https://www.walkhighlands.co.uk/cairngorms/loch-an-eilein.shtml Coire an t-Sneachda
https://www.walkhighlands.co.uk/cairngorms/coire-an-t-sneachda.shtml Ryvoan Pass
https://www.walkhighlands.co.uk/cairngorms/ryvoan.shtml or Meall a' Buachaille
https://www.walkhighlands.co.uk/cairngorms/meallabhuachaille.shtml Heading west, Glen Affric has a couple of lovely short walks in the ancient pine woods
https://www.walkhighlands.co.uk/lochness/glenaffric.shtml and
https://www.walkhighlands.co.uk/lochness/Dogfalls.shtml You could also visit Torridon, one of my favourite parts of the country - both
https://www.walkhighlands.co.uk/torridon/coire-mhic-fhearchair.shtml and
https://www.walkhighlands.co.uk/torridon/Mountaintrail.shtml are superb.
Hope that gives you a few ideas - hope you have a great trip!