In reply to Beardyman:
The Fisherground campsite looks pretty good for families. I've never stayed there, but with family friend who live near Boot, I have wandered past/through plenty of times. There's a Caravan Club site up near Boot as well, also looks pleasant. No further than 20 mins walk to the nearest pub from either (George iv and Boot Inn respectively).
Fisherground is a good family spot, as are the Heron stones further up the valley (park near Brotherilkeld just before Hardknott). Lovely spot with plunge pools close by. A little bit of a walk, probably half an hour(ish).
The Langdale circuit may be worth a look, and the Honister boulders as already mentioned. Also Badger Rock/Little Font in Kentmere, Sour Milk Ghyll Boulders down Borrowdale or Carrock Fell depending on how the bracken is looking (I haven't been to Carrock for a few months now).I also believe Dunnerdale has some bits and pieces and it's a very family friendly valley with a short drive from Eskdale Green.
It really depends on where you end up staying, as it can be a long travel between valleys which are only a few miles apart as the crow flies.
Hope that helps a bit. I'd check out Lakesbloc for really in-depth information.