Honister Slate Mine is not just England's last working slate mine! It offer lots on adventurous options including various Via Ferrata routes, canyoning, climbing in the mine and of course mine tours. There is also a shop for all things slate.
Ullswater Steamers offer lake cruises between Pooley Bridge, Howtown and Glenridding. You can combine them with various walks, souvenir shops and cafe trips to make a great day out. Be aware that it can feel cold out on the lake!
The closest start poing is Pooley Bridge.
Keswick
If you’re going to get a bit damp, why not go the whole hog?
You can also consider most of the ‘Historic Houses & Gardens’ outlined on that page as suitable for rainy days.