As someone who is from Skipton, although one who lives abroad now, I think the Travelodge just north of town is a great idea. 20 minutes walk into town. Bizzie Lizzie's is a very good fish and chip shop, although good kebabs can be had elsewhere (name of establishment escapes me but it's Turkish run, unsurprisingly). There are stacks of good pubs on the High Street, Woolly Sheep, Black Horse, Red Lion to name 3, and one I think will really appeal to cyclists, called the Narrow Boat, which is up a side street off the High Street. Skipton is a great little place and I'd be surprised if a visitor disliked it.
When I visit Skipton next year I think I'll stay in the Travelodge. I'd forgotten it was there so thank for reminding me. One thing, though, you say they allow bicycles in the rooms. Do you think they'd let me take my motorbike in?