Back to the caving, in the Dales, to lob in a few suggestions;
For some easier caving (well, easy as in going down multiple pitches without having to go back up) there's the Simpson or Swinsto through trips, mix of walking and crawling with only a short pitch up to exit.
Or for a fair bit of climbing down scaffold, you get a pleasant streamway and nice formations in Notts II (although that's another one that requires a permit, so you'd have to plan that one in advance a little! although if midweek there shouldn't be much trouble getting a permit)
Think someone said Alum Pot above, big open shaft (spacious and scenic) but the classic view out across it is obtained by descending Lower Long Churn Cave and popping out part way down the shaft, then you continue down some more pitches before heading back out and having a quick run up Upper Long Churn, nice little trip. (and no permits here, just a small fee payable to the farmer)
Guess it depends what kind of caving you enjoy!