One thing to consider, it may be cheaper for you to live in London than in the burbs. We currently are living outside of London. My DH commutes 1.25hours each way (we have a direct train from Hitchin-Kings Cross) and pays extortionate train fares. Those fares added to our council tax (which is higher than almost everywhere in London) means it is cheaper for us to have a £1200/m flat in London than to live in a £620/m one in Hertfordshire.
Danielle - Your DH has my complete sympathies - I commute every day on the Thameslink line. And FCC is sh*t!!! Of course, it's not like the Tube has been doing well recently, either...
But this is a very good point these days. In some cases it is a lot cheaper to live outside and commute in, but with rail prices going up, you should definitely consider the cost of commuting alongside the cost of your housing.
Anyway, as everyone else has mentioned, there's a lot more you need to be considering when deciding on an area to live in. And when it comes to it, everyone is going to have a very different opinion about best places to live, so be mindful that our suggestions will be a bit biased. For instance: a lot of my friends love 'trendy' east London - I find it a bit dirty. I love south London, but a lot of people wouldn't even consider living south of the river.
Some people have mentioned getting a tube map, which is good to start with, but I'd recommend using the Oyster rail map, which will include overground and national rail services as well:
http://www.tfl.gov.uk/assets/downloads/oyster-rail-services-map.pdf (a bit complicated, but very worth considering as it can provide other routes for getting around).