Further suggestions in South West Cornwall:
Trevaylor Woods near Penzance is fab for suicidal kids, loads of fallen down trees straddling a river. Some non-Health and Safety tested rope swings too. DP and kids have also camped there (I was busy that day).
The Marazion end of St Michael's Way is great. We do a short walk, about 45 mins, from the A30, across some fields, then have to cross another yuk/busy road but after that, it's woods, followed by bridge over marsh, railway crossing then riverside walk until you hit Marazion. You can't beat walking over to St Michael's Mount when the tide is half in/out, so you have to wade. You could avoid the road crossings but starting from Marazion and stopping at the pine wood.
Also beach at Marazion is very flat and, as far as I know, no bad currents, so it's brill for the youngsters if they are nervous of waves, and it's quite warm. Bit too much seaweed and too many flies for me but it doesn't seem to bother the rest of my gang.
For the birdwatchers, there is a fab nature reserve at Hayle Estuary. A lovely flat walk where you get to see all sorts of sea birds, including my fave herons and little egrets.
Cape Cornwall is thrilling, especially in rough weather. Hard walk up to the top and not good for people with vertigo but probably not dangerous with reasonable care. Drive there via Zennor (just outside St Ives) and enjoy the spectacular views.
Or get the 300 bus, I think you can get a round trip ticket from Penzance or St Ives (and probably from all the stops along the way) and get on and off at good bits like Geevor mine or Lands End. It's a long journey (over three hours) but that's part of the point.
Also the train journey from St Erth to St Ives is short, about 15 mins, but stunning.
Jubilee Pool in Penzance is freezing but fab, and a real suntrap for Mum to sunbathe while kids play in the open air sea-water pools, main one deep (well over waist height for 5'8" me) but little one ideal for younger kids. Also, great cafe attached and a nice promenade to walk along (if you are brave go at high tide on a rough day and get splashed by the waves) with an amusement arcade and children's playground at the other end to where the pool is. Also a bit further along a skateboard ramp and a boating pond (for playing with model boats).
Trevaskis Farm near Connor Downs/Hayle is free entry, you can walk around a proper farm, see all the animals (not a petting zoo type thing, you just get to look) and they have 'pick your own' and a really interesting vegetable garden. Also, a great farm shop, we get most of our meat from the butcher there. And there is a restaurant where they use mainly their own produce.
I'm sure I could think of more for those who haven't fallen asleep yet!