Hmm.. not really, the nearest would be
Cresswell Crags which is just south of Sheffield.
I had never heard of it before it turned up on the tentative list if that is any indication its renown. I would also be exceptionally surprised if it even made it off the bottom of list of UK tentative sites, seems a really odd one to me, it is not exactly Altamira or the Lower Awash Valley.
Jodrell Bank observatory is also in the region, to me it seems more interesting
If you have your own transport the
Lake District could well be viable.
From Leeds I would say the most interesting non WHS related places are
York (could have been a WHS if they were in the mood for it in the 80's) and
Harrogate (en-route to Studley the Turkish baths are a nice treat). Otherwise
Haworth (for Bronte sister associations) and
Hebden Bridge are also nice.
I don't know much about Manchester (aiming for a first visit soon) but that may also appeal for it's museums and cultural life.
Food wise Bradford is well know for its curries, and if you are in Yorkshire on a Sunday it would be rude not have the eponymous
pudding with a roast.