Here is a great place to find out what is going on in and around Manchester.  It is an 'Artslist' with details of theatre, exhibitions, festivals etc.  There is a free newsletter which is geared towards the areas you specify you are interested in.  You can also look for events that are specifically family friendly here.

Family friendly events in Merseyside can be found here.

Another great place to look for events in and around Chester (even into North Wales) is here.

Sarah