In reply to Ruth:
Grid - 3505, or about 354057, eyeballing it. Marked as 'caves' on the OS Explorer, and Rydal Cave on the BMC map. See also Loughrigg Fell in Wainwright guides under Loughrigg Fell 7. Altitude about 130m, so maybe 75m up from wherever you parked. The cave isn't obvious until you're on top of it, but then it's very obvious, and very large! Good views, but no sheep that I can think of (my toddler loves sheep...). Tea shop ar Rydal Hall, though a short walk uphill from the road which may not be appreciated at the end of a walk. Would be surprised is there isn't an icecream van at the Rydal Water parking 350064, and I think the approach might be easier going for short legs from that direction.
For more like 4km with an intermediate stop, park at the P&R, then head out towards the cave, and down to Rydal Hall tea shop. Rest. Return via the obvious path above the road (aka the coffin path, wooded, possibly not the best views, but I was running, it was late, and getting dark, so my memory may be jaded). If tired, the bus definitely stops at Rydal Hall, and I would imagine it stops at the parking too.
Subbing for any more ideas, I'll be up there with my just-gone-3 year old later in the summer....