Regular places in the local area we do in the summer are New Brighton, Port Sunlight, Antony Gormley statues at Crosby and Sefton Park.
Lots of museums as well which are always worth going to go and many are free - World Museum, Liverpool Museum and Maritime Museum.
If they're really young then Farmer Teds or Apple Jacks farm aren't bad options either, but can be incredibly busy if it's warm.
A bit further afield, the Ice Cream Farm (Tattenhall), Shire Pony Centre (Tarpoley) and Candle Workshop (Beeston) are good in Cheshire.