I live in Keswick, and would add a vote for a back of Skiddaw ride- from Newlands I’d go up the pass and over to Buttermere, because it’s lovely, then round past Crummock water and through Lorton towards Cockermouth. Take the back road past the hospital and Isel bridge to Castle Inn, then Ullock, Hesket Newmarket, mungrisdale and back on the gated road under Souther fell to Threlkeld and home via Burns/Castlerigg stone circle. Easily lengthened or shortened, but once you’re committed to the back of Skiddaw there aren’t any short cuts. Hilly, with a couple of steep ramps, but not too crazy. That’s a big ride, maybe too much, shorter and easier if start with Whinlatter instead of newlands.
You’ve got to ride honister from buttermere at some point in your stay- that’s the hardest pitch in the immediate area of Keswick.
Avoid A591 and A66 on a weekend, not much fun with traffic.