In reply to mason_7:
Are you limited to only Fort William or Aviemore? The Glen Brittle campsite on skye is a great place to stay if you haven't got a car and want to do climbing and walking straight out of the campsite. Othewise I guess some climbing on the Ben and a backpack around the mamores/Grey corries or walk into Loch Avon in the Caingorms and do some climbing from there.
There's not a lot of climbing this way but the best thing I did in Scotland without a car was getting the train to mallaig, boat to Inverie on knoydart and then walking out to Glennfinnan. Gorgeous remote walk (from 3 to 5 days depending on what you do) and then you could do some climbing afterwards. I'm sure a bunkhouse/hostel would be more than happy to let you store stuff.