World Museum, Liverpool
Five floors, free, and it covers three things small children reliably love: giant dinosaurs, an aquarium and a space gallery. The best wet-weather day within half an hour.
Croxteth Hall & Home Farm
Liverpool, Merseyside
A working Edwardian estate farm - rare breeds, enormous pigs, a walled garden - inside five hundred acres of free country park.
Farm entry is cheap enough to be a habit rather than an event. The adventure playground in the woods is the other half of the visit.
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Also in Liverpool
Speke Hall
A Tudor hall with woodland walks, a maze and a natural play area in the grounds. Free if you have National Trust membership, and the indoor house is a good rain fallback.
Museum of Liverpool
The city's story with an overhead railway carriage to climb aboard and Little Liverpool, a dedicated hands-on gallery for under-6s. Free, on the waterfront, and the window views are half the fun.
Merseyside Maritime Museum
Titanic and Lusitania told in the city that crewed them, ship models, and the Seized! customs gallery in the basement where kids hunt smugglers. Free, and the Albert Dock outside is its own event.
Mersey Ferries River Explorer
The famous ferry across the Mersey run as a 50-minute sightseeing loop with commentary, and the honest truth is kids love the boat more than any museum. Hop off at Seacombe for Eureka! next door.
Calderstones Park
South Liverpool's favourite park: lake, playground, ancient trees and the Storybarn, The Reader's hands-on storytelling space in the old coach house. The neolithic Calder Stones are older than Stonehenge, which is a good fact to deploy.