My boys (6 & 4) went to Old MacDonald's Farm at Brentwood ( we're in Basildon) with their Grandparents inthe summer hols and they're still talking about it! Got all the usual animals and some more fairground type attractions and its all included in the price.
The Salvation Army farm at Hadleigh is good too. Much smaller scale, but the children can feed the animals, there's a small maze and sand pits (in summer only I think) and it only costs about £1.50. Fantastic tearooms too.
Mum and Dad (I'm starting to fee guilty here) have also taken them to the Historic Dockyard at Chatham and Duxford Air Museum, last summer and they both talk about those too, although they are further a field and might suit slightly older kids.
We find a trip on a train is always enjoyed. Doesn't really matter where to, but you could go to London and then you can see Tower Bridge & the boats at Tower Hill and even go on an underground like Ernie too!
They have also, always loved Southend, in all weathers. On a cold, but sunny day, we have even had a picnic on the cliffs at Westcliff, where you're sheltered from the wind and in full sunshine & it's lovely.
Another good one is wellies on and throwing stones in the water. If you go all the way through Southend and out the other side and turn left at the watersports centre, there's South Church Park, which has a large free car par and a lovely play park. So our day might go. Swings, walk round the boating lake, kick a ball on the playing fields, lunch in OK cafe (or picnic), down to beach to thow stones, then walk along prom, with children walking on sea wall, which for some reason they seem to enjoy more than ordinary walking There are no arcades at that end, which from our point of view is a blessing.
There's the SeaLife Centre at Southend too, whcih the boys (and their Dad) have loved since they were very young, but it boes me to tears. I'm often out voted, but I don't think it's very good value for money, but is is somewhere to go when it's raining.
Just to get out in the fresh air for a while, try Weald Country Park, just north of Brentwood. If you take a bag of carrots and some bread you can feed the deer and the ducks. The deer devour the carrots whole and I remember my DS2 laughing at them until he fell over when he was about 2. Great kite flying there too.
I'm on a roll now. I hope this helps, but if not I'll have another think.