Bewilderwood is brilliant - Its about £13 - We had to pay full price for DD (5) cos she was tall enough to use everything and she did - Its amazing, little boat rides, den building, big slides, tree houses. She loved it - We spent about 5 hours there and could have easily spent longer.
If you want a lovely pub lunch at the side of the river, visit the Rising Sun at Cottishall, its about 5 minutes from Bewilderwood and lovely if the weather is nice. The food is gorgeous.
Banham zoo is lovely but is about an hour or just over away from G Yarmouth. They have started doing an animal passport thing where you hunt for stamps around the zoo and get a medal. DD loved doing this.
Hire a boat and go on the Broads for a few hours.
If you want a nice beach, I would recomment Gorleston or Caister.
We did Cherry Tree at Park Dean - Not too far away from Yarmouth or Caister but also quieter - Has a small pool, food, evening entertainment, play areas etc. Its like a Haven but not quite there if you see what I mean, but its cheaper as well. Only cost us £350 for a week at easter in a 3 bed deluxe
We also hired cycles a few years ago (from Bewilderwood carpark), some lovely cycle routes, many off road.
Don't do the aquarium - £14 a person and you will be in an out in about 30 minutes