Hi Elizabeth!
The first thing to realise is that Scotland doesn't have a 'climate', we only have 'weather'

October can be very nice, but it can also be cool and damp and there's no way of knowing what the weather will be like more than about a week in advance.
If you have good sleeping bags you would be fine in a tent as overnight frosts are unlikely until November.
As far as what part to stay goes, well you've already travelled more or less all around Scotland so I'd suggest you take your pick, though anywhere in the Cairngorm National Park will be beautiful with autumn colours in October.