We've just come back from Cornwall and have a few recommendations and also ones we wouldn't go to again.
Lanhydrock House (NT) nr Bodmin - lots to do if the weather is a bit iffy. My DC did the garden trail (took them about 1 hour). Nice cafe and icecream kiosk. House is good but not great for toddlers. Loads of space for children to run around.
Cotehele (NT) nr Saltash - huge site - can't see everything in one day. Gorgeous medieval house, grounds go down to the Tamar. Lots for children to do. Lovely cafe.
Daymer Bay beach, Camel Estuary - nice beach shop and cafe, parking £3.50 for the day. Some good walks across dunes to St Enedoc and, if tide is out, you can walk right round to Rock. Coast path to Polzeath also.
Rock - good if you can get parked anywhere near. A bit pricey in the cafes though.
Old Macdonalds Farm at Porthcothan - brilliant value for money for small children (up to about age 10 max). Loads to do while you relax on the terrace/in cafe with a coffee and good book. Nice cafe and little shop. No good in the rain though.
Trevathan Farm Shop, St Endellion - fab cafe, and shop. Outdoor play area, some animals. PYO strawberries.
Definitely would not recommend Springfields Fun Park and Pony Centre nr Newquay. It was not value for money, was dirty (cobwebs everywhere in the play centre and cafe), looked run down, shabby and a huge flock of pigeons has invaded the outside play area. Really needs some sorting out. Disappointing and the cafe was expensive for what it was. No homemade cakes, very little choice of food. Dairyland also nr Newquay is much much better.