Sefton Park and Calderstones park are lovely. As someone else has mentioned, Lark Lane just outside Sefton Park has a really nice feel to it for a coffee/lunch/tea etc.
The Museums are free
It’d be worth a look around The Albert Dock, lots to do around there and you’ll find a lot of The Beatles stuff around there too along with Matthew Street.
Bold Street has some really quirky independent shops and lots of restaurants.
If you’re there at the weekend, stay away from the McDonalds at the top corner of Church Street near to Liverpool Central station-I took my 4 year old in for a wee a couple of weeks ago and it honestly felt like I’d walked into lunchtime in a secondary school. The one near Liverpool one is better during the day.
If the weather is nice, it’s definitely worth a trip on the Ferry, there’s a nice walk up to New Brighton and there’s also Eureka Science Museum inside the terminal over on The Wirral side.
Knowsley Safari is free for children during half term but it’s quite a way out of the city centre and you’d probably need a car.
We always enjoy Croxteth Park farm, but again, you’d probably need a car to get there or at least a taxi from the City Centre. There isn’t a train station nearby. You could get the bus, (which would be absolutely fine but some people would probably say to avoid the areas it goes through).
I hope you have a lovely time! I love living here!