I'd like to start by thanking this wonderful community. I've already learned a lot from your ideas and suggestions to others.  Clearly a lot of options when visiting Scotland, and my family could use some guidance to narrow them down. 
Details:
Our kids are 8 and 10, and prefer to climb a rock vs look at old paintings.  My wife and I love history, good food, and a good walk in nature or small towns. 
We arrive in London on Nov 23, and then we're going to take a regional jet to one of the three airports, spend about six nights exploring whatever we can, and then return to London for another five nights before heading home to California. 
I would like to get a taste of the "authentic" countryside, whatever that means. 
We plan to rent a car to be more flexible. 
Kids prefer a home base to return to rather than a new place to sleep each night.
We might be interested in a farm stay, but the late Nov options seem limited. 
Question:
If we were to pick one home base in Perthshire or the Western coast to get to know for several days, which place would you recommend?  Ideally also be a place that is nice for cozying up to a fire, with  good pub or restaurant nearby.