I have a 2 year old daughter and have just taken annual membership for Court Farm for me and her. Cost me £23. She is free. She loves it there and there is plenty for her to do. It is a working farm, with lots of animals. You can ride the horses and feed the lambs. There is an indoor playarea and a large outdoor area too with a maze and tractor rides. Alot of the above are not available in the winter months, but the farm is still open and for the price you can't go wrong.
As my daughter is still little I am not sure how much she gets out of places like Bristol Zoo, whereas Court Farm is ideal.
Give it a go!