The way we went about our search was based on the tube lines (because we don't plan on having a car): The tubes are broken into Zones, Zone 1 being the city center and Zone 5/6 being quite a bit further out. Area's in Zone 1 (including Kensington) tended to be pretty expensive, so we eliminated those. We found as you go further out of Zone 1 the areas got cheaper (with some exceptions). We also wanted to be close to the city so our commutes would not be too long therefor we decided on looking at places in Zone 2 and 3. I cannot confirm this, but I do believe if you live outside of Zone 3 and travel into Zone 3-1 the tube ride gets more expensive. To make a long story short, here are our top 3/4 areas (based off tube stops):
Greenwich (Borders Zone 2-3) - We both really loved this area.
Islington (Zone 2 Angel Station)
Highbury (Zone 2)
Arsenal/Finsbury Park (Zone 2)
There were a few more and some we really did not like, but I can't remember them off hand. These are all based off first impressions and might turn out to be really bad places to live. We ended up deciding that employment will drive where we will end up living since just about every place we saw had it's goods/bads.