Welcome from Portsmouth. I've walked C2C twice, first one way then the other. Given a choice I preferred the hike towards the Lake District, for me doing the best bit last. I did enjoy the Lion Inn though, especially on the night when a USA man held court in the pub and told all of us customers about his business of growing tomatoes, the different varieties, shipping problems, timing and so on. He was a real enthusiast!
My best C2C was when I hiked with some Walking Forum blokes few years back. We started from St Bee's, crossed the Lake District and when we arrived at Keld in the centre of England, they carried on to the end of the C2C, whilst I turned south on the Pennine Way to Edale. For me it was two walks in one.
Do linger on High Street and try to soak up the Roman history of it, its claimed that chariot racing took place up there. Not sure if its true but I like the idea of it.
My only disappointment was upon arrival at Edale, the pub served me a disgusting meal! I sent it back and they then without quibble, they provided me with a really good one.