I'm a bit further North than you and I'm currently doing up my new gaff in Cumbria (between Appleby and Shap) and am also new to the area.
If you are into hill walking get yourself up Blencathra/Striding Edge etc. Get a sailing boat or a canoe/kayak for going on the lakes. Get a mountain bike, tons of decent rides around here. Learn to fly fish, everyone seems to be doing it. Likewise get a shotgun, join a shoot. Visit my brother in law's pub, it's won awards and the food is top: George and Dragon Clifton | Go to a tourist info spot and grab a load of leaflets that interest you, there is a James Bond museum which is quite cool. If you have kids take them to Rheged discovery centre in Penrith, there is a pretty decent playground which is free and loads of activities to keep them occupied while you sample the beers. Take your missus to Abbot Lodge Farm, where they make their own ice cream from their herd of Jersey cattle. Again the kids will love it.
When you get bored of all that, become a cab driver and go on a shooting spree around West Cumbria.