It depends on the child. At that age, my DS was very easy-going and we could take him anywhere and he would be fine. He did really enjoy the Pooh characters at Crystal Palace.
I would say that, if feasible, you should find places the child would enjoy besides just the typical children's fare. Kids that age generally are not used to eating chicken fingers, hot dogs, french fries, etc all the time. Not to get too TMI on you, but DS had some intestinal issues after his first trip.