Moved this from the other post:
Well, it depends on the job you want to be honest, you'd be surprised how difficult it is to get a job in London at the moment. But aside from that bit of pessimism, London has so many places that are great. I live in a suburb in West London that is slowly growing (Hanwell) and is pretty family friendly. It is also close to most forms of major transportation, including Heathrow.
The east and south/east (Shoreditch, Bethnal Green, Camberwell, Peckham, Brockley, Dulwich, Brixton, Streatham, etc) are all up and comers and would probably be in your price point. They are also gentrifying quickly, so there are hip cafes, restaurants, shops, cinemas, urban farms and places for families to grow. Unless you're in zone 5 or up, anywhere you are you'll be able to go to museums without much hassle. I live in zone 4 and I go to museums all the time, especially since there are museums, historical properties and points of interest all over the city, not just in central London (for example, I live next to a canal, 3 parks and also live close to Ealing Broadway, Chiswick, Kew Gardens and Richmond Park)
The London Overground has also made it easier to get around in more of the outer areas in the southeast, though most Londoners deal with long commutes to work and play. It's just a fact of life that it will take you ages to get from one place to another unless you tend to not leave your area. I haven't driven a car in the six years I've been here, and my husband only drives if we're going on holiday to the countryside. You don't need to own a car in London, and there are even car share organisations if you find that you need one for a big shop or an Ikea run.
London (like the majority of England) on the whole is safe, safer than most cities in the US I would say. But unless you live in a place like Chelsea or Mayfair, there will be a mix of poor and middle class people, which I find fantastic and a big change from the US. I also think that if you don't go looking for trouble, most likely trouble will not find you. I've never really had any issues while living here, and I've lived/hung out in places like New Cross (which I would love to move back to) and Peckham, which have bad reputations (though both are gentrifying rapidly).
I can't help so much on property search, since I lucked into my current place, but friends have used Zoopla, Right Move, Gumtree in some cases, and there are newspapers with property sections as well. I know I’m missing some big ones, so hopefully other people will be able to help with that. In my experience, hostels tend to be student-catered, but a google search led to London House Hotel in Notting Hill. It seems a bit expensive though, now that I've looked at it.
Hope this helps a bit!