Bexley is a civilised suburban area of South East London. I don't know it very well from personal experience, but it's quite well known to South London dwellers in general. Here is my list of pros and cons, so far as I understand them.
Try looking it up on the web.
Pros
Near enough to central London
Far enough out of central London
Near enough to the dreamy and tranquil beauty of the Kent country side (known as "The Garden of England")
Moderately civilised
Busy, suburban lifestyle, if you like that sort of thing
Easy to get to continental Europe - close to Waterloo (trains to Paris that go under the sea), acceptable drive or train ride to Dover (sea ferry to France)
Access to the London job-market
Demographics generally affluent, professional types (if you like that sort of thing)
Cons
Property prices out of this world
Affordable places are small - not much space in house or garden for sensible money
Not for you if you want peaceful country life
Not for you if you want the real big-city experience: you need to live closer in for that!
Wrong side of London for visiting the North and West of England, Scotland and Wales.
Quite close to the East End (read the Bronx/Queens) - apologies to any East-enders out there
If you're attracted to the Kent countryside (who wouldn't be), but still require easy access to London, you might consider moving further out. I would recommend Sevenoaks, Tonbridge or Tunbridge Wells. Still expensive properties but you get much more house for your money and have shorter journeys to the real country side, whilst still maintaining easy proximity to London.
Further out still you get even more choice, but the pick of them all is Canterbury - a stunning place. It is too far from central London for an easy commute (although some people do), and hence property prices are MUCH lower. But on the upside you get the experience of a REAL historic cathedral city and a somewhat more tranquil lifestyle.