Best place to live for young family - Central London or not?

Hi there, we are an Aussie family living in Thailand who are about to move to London.  We lived there before kids so have some idea of areas but its a new challenge with kids.  I have a 3 and 4 year old so need to be in a safe suburb with good schools.  My husband will work near Liverpool St Station.  We have been looking at North London and South East London.  We use to live in South West London but are hoping for a shorter commute this time round.  Our other thought is somewhere like St Albans.  So my question is would you recommend central London or out of central London? Any suggestions of areas would be much appreciated! :)

Depends on your budget. Central London is a very very expensive place to live.

We would like to keep our rent budget to 2000 pounds per month if possible.

2000 is an OK budget if you need a proper flat (with 3 bedrooms, unless you want to put your two kids in the same bedroom). Safe area, I would suggest zone 2 (Fulham, Kensington Wandsworth are good in zone 2). Don't go to Brixton, Hackney and Peckham, those are dangerous areas, esp for kids. Of course unless you want to live in very good areas in zone 1, like Sloane Square (Chelsea).

My son lived in the West End great location for just under £2000 a month two years ago.
For this he had a small lounge one bedroom kitchen and bathroom.

There are no houses in central London that you could afford for a 2 or 3 bed flat you will be paying £3000 plus a month plus rates heating elect. There is no parking in central London with restrictions on parking for delivering even your furniture.

I think most of the good areas you are going to have difficulty paying the monthly rents.
Try an agency is your best bed and research fully the areas they are offering because even in decent areas there are some dumps.

Make sure you have plenty of money for all the extras in some of the better areas.