I can't recommend Twin Lakes highly enough - there is more than you can do in a day and it doesn't matter if its wet as there is loads to do inside. Once you've paid to go in everything else is free. The food is a bit better than you normally get at this sort of place (you can take a picnic) and its not too expensive. All the rides etc go by height so you may need an adult to go on as well. I'd recommend going as soon as it opens as it does get quite busy then you can do the rides first and spend the rest of the time at the things you don't need to queue for.
You'll see the £50 ticket offer on the website and if you have time to do any of the other three things it will save loads. The other attractions are all good as well.
Space Centre - a must for anyone interested in space, exhibits and interactive stuff. I think the tower is really interesting.
Conkers - excellent (mostly) outdoors and the playground is really good and all boys like the train ride. I think the food here is dear but again there is plently of room for picnics. The indoor area is small but its good - my boys love the dark slide (you can go on as well) and the indoor play area.
Snibston - this is possibly better for a bit older children but again there's interactive stuff and a short train ride (a real train). This is mostly science related but there was (when I last went) a really good fashion exhibition which I think is a permanent one.
Actually we will be going to all these places ourselves over the summer break - the East Midlands is pretty well served for childrens activities.
I hope this is the sort of thing you were thinking of - if you'd like recommendations for any other sorts of places (National Trust/parks etc) just say