Not got time right now to provide links but for information: NFTFH book is excellent for information on the harder trips and the CNCC produce a rigging guide for all the caves they have re-bolted. Online there's Cavemaps for surveys, Braemoor for descriptions/guides and more recently re-bolted caves the IC-Resin anchor site has a few topos.
Some of the fine caves, personal opinion obviously, in no particular order.
Meregill - a fine clean washed feast.
Lost Johns' Cave - a few options for the vertical and a good stroll at the bottom (Boxhead and Cracker provide interesting alternative ways in/exchanges) or do lots of squirming through to Notts II. It's far easier to descend Committe Pot/Iron Kiln tackle free and enjoy the fantastic Notts II streamway the easy way!
Pool Sink - best way in to Ease Gill IMO, can be done in-out or pull-through/exchange to other entrance (lots of choices) - pre-rig Lancaster for exit after pull-through if you're short on bodies or exchange with Cow if you've plenty so you can sample the main drain. Plenty of variety, the only problem being route finding...
Birks Fell Cave - not much vertical but loads of great caving, a satisfying long trip.
Penyghent Pot - classic sporting pothole.
Alum Pot - it's a stunning open shaft, direct or go via Churns to enjoy that well known view.
Long Kin East Cave/Pot - maybe, I liked it - pleasant streamway and big shaft, can be done as exchange with Rift, doesn't seem as popular as other nearby places (like the equally fine Juniper Gulf) though.
Manchester/Goyden Pot- start in one, through, round and out via Church Pot perhaps, plenty of horizontal variety.
There's plenty of other great trips to be had though, depends what you like I guess (easy/hard, wet/dry, vertical/horizontal, short/long and the list probably goes on...)