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My daughter lived in Cumbria (Penrith) and Lancashire for 10 years. I visited annually. Cumbria and the Lakes district are wonderful. Too many great opportunities to list but span Appleby, Hadiran's wall, Carlisle, as well and the entry point to the Lakes District. Yorkshire Dales (Sedbergh mentioned above is a very large area on the other side of the M6 from Cumbria's Lakes District. I've found it hard to plan an itinerary into the Park. My trip to Ingleton and Settle were very productive. Your Cumbria destination is very accessible from either Manchester or Edinburgh. Glencoe is a much longer, harder drive but very scenic.
If you come in to Edinburgh, you will want to give it at least a day in its own right unless you've already been there.