Get the ferry across the Mersey and go to Sealife or Eureka museum across the water or just a wander and an ice cream and back
walk around Albert dock, there’s a boat tour around the docks which is every 15 mins or half an hour, think the duck tours have stopped. Slavery and maritime museums are excellent, there’s the dock masters house too which is good, again all on the dock. Smugglers cove restaurant is a really well done themed pirate restaurant. The big wheel is also on the docks.
walk around the Liverpool one shops/restaurants. Bold street etc for more excellent restaurants and shops.
bombed out church at the top of bold street is cool too.
keep walking up the hill to either of the cathedrals, each very different. You can go in the catacombs of the catholic one or climb to the top of the Anglican and see for miles.
world museum and St George’s hall are great too. There’s a museum under St George’s if it’s still open from when it was a courthouse, that’s different.
open top bus tours.
ghetto golf down by cairns brewery etc.
food wise I’d recommend Duke Street Market or Baltic Market for different amazing concessions in one place, most places on bold street too.
3 year old would like Imagine That if you need to divide and conquer - it’s a cross between small world role play (with tv studio, shops, theatre, construction etc), an art studio (paint on a real car and other crafts), science experiments, and slime factory. You go through the 4 different rooms. Thats by wavertree technology park.