First, the Pie Shop in Gosforth is not to be missed...
Punchbowl at Crosthwaite is nice.
L'Enclume at Cartmel.
The Samling near Windermere.
Linthwaite House Hotel near Windermere.
Masons Arms at Strawberry Bank (some good roads).
Kirkstile Inn Loweswater.
Lyzzick Hall Hotel near Keswick.
Armathwaite Hall Hotel, Bassenthwaite.
Nicholas End Marine, Portinscale, for the view and superb breakfasts and homemade scones etc (not posh, but I like it).
Try that for a start.
If you want more suggestions, just say.
For a day out, the Ravenglass to Eskdale railway (the Ratty) is great fun, close to Gosforth and there are good pubs.
Muncaster Castle is also close to Gosforth and a good day out.