Can up you get to Southport?? If so that could be a good day out, lots to do & not all expensive -
they have Splash World, a big indoor swimming & splash pool complex with slides & lots more
The Pier has an old fashioned amusement arcade museum on the end of it, laughing Policemen etc etc, you can take a tram down the length of the pier
If its warm enough, picking razor shells & bird watching on the beach, followed by a donkey ride
They also have another big fairground that I forget the name of, but lots of suitable rides for a 6 yr old & you can pay a flat price for a book of tickets & worth looking out for vouchers in the local news.
Lots of good reasonably priced restaurants, old fashion sweet shops & shone great fish & chips & some excellent ice cream too
My DPs live there & I've had many a good day out with DD, especially when she was younger, Splash World is still her favourite swimming complex & she's been to a lot over the years
HTH