You really want to try Ainsdale Beach, its probably the best in the region or Formby Point is excellent too.
Just watch out for the odd Mersey Trout if you bathe!!!
Also, a nice little sandy alcove with a bit of a bay mixed in is Hightown, you will have to look hard on the map though to find this place, it lies between Crosby and Formby on the Liverpool coast line.
Whats wrong with Morecambe?!?!?!?
Anyway - as others have said Formby is nice but nowadays the north wales coast is very accessible and only about an hour away. Colwyn Bay, Prestatyn, Rhyl and Llandudno all have nice beaches.
You could also try the Wirral at Wallasey and West Kirby.
You could always go to the big B&Q in Trafford Park, buy a couple of bags of sand, walk down to the ship canal and pretend!