Hmmm, that's a tough one. Where is central for everyone? I guess the city but not sure what you had in mind. Do you normally go to a cafe or restaurant? Or do you go somewhere with more focus on occupying the LOs?
Covent Garden comes to mind with plenty of cafes/eateries AND the Aussie Shop to stock up on the odd snack from home.
I've done a search on family friendly restaurants and it came back with the following suggestions - My Old Dutch (in Holborn), Cafe Rouge (Covent Garden), Smollensky on the Strand (Sundays given over to families includes a clown), Belgo (Covent Garden) to name a few.
I was wondering about a childrens indoor play centre but I think the closet central one I found was the Blue Kangaroo in Fulham.
Another idea I had was to visit a farm but again they aren't in the city so to speak. Some I found were Hackney City Farm, Mudchute Farm (Docklands) and Spitalfields City Farm. All of these are further East than they are central.
There's always one of the Royal Parks as well - St James, Green, Hyde, Kensington or Regents Park/s.
Just a few ideas, what do think?