Just got back from a fortnight in St Ives, so very jealous! Hope you have a wonderful time - the local weather can be very kind, it can be raining up the hill and not in the bay.
Nice little cinema in St Ives showing 'cars' - that'll pass an afternoon well. The other suggestions look lovely too.
Make sure you've got your wellies and have a walk along the beach, making a collection of interesting things. Watch out for the seal in the harbour, particularly when the fishing boats come in. Watch out for the seagulls on the harbour beach, they will steal the food out of your hand unless you hold it close to you. Seriously. Have a darn good time. There is an excellent Indian takeaway just a few doors away from the cinema - highly recommended. We had loads of take outs, all delicious.
Free internet access from the library near the cinema too and some great kids books to look at.
The Tate was great, but there are no sculptures/installations this year, which my children usually love.
The roadworks are a bit of a nightmare each way - around Indian Queens on the A30. You're going midweek, so hopefully it shouldn't be quite as bad.