Great Douk Cave
Long Churn Cave
Birkwith Cave / Old Ing Cave etc
Manchester Hole / Goyden Pot
Short Drop Cave
Skirwith Cave
Ibbeth Peril
Dow Cave
Crackpot Cave
The above caves can get wet so not great choices right now.
Runscar Cave / Thistle Cave etc - Runscar may be wet, Thistle is ok IIRC - lots of other little holes around Ribblehead to play around in.
Wretched Rabbit - apparently gets wet but I've seen the main stream in flood and still got out this way without a problem.
Wet weather options;
Mistral Hole is dry, although you need to like crawling.
Attermire Cave - and surrounding other holes.