I moved to LA with DH's work earlier this year, 2DC now 4 and 1. No experience with Singapore
Do you know where in LA you might be? I only learnt to drive a few weeks ago - it has made life a LOT easier but we rented a house close to both DH work and DS preschool so I walked everywhere, and we're on the border of Santa Monica which has a good bus system.
LA is much like London and other major cities in terms of safety - where I live we often leave our door unlocked when going out, windows open at night (single story house) etc. but there are probably areas I wouldn't go to after dark alone - the perceived gang threat is much reduced however and very specifically located. Most of the city is fine.
It's an odd city though - I'm a total city girl, grew up in London, adore NYC, Chicago, Madrid, Paris, Prague, Barcelona etc but LA is altogether a different beast. I do feel pretty settled, which I was expecting to happen so quickly and is absolutely down to the friends we've made here making such an effort and taking us under their wings (some were friend's of friends, some DH met through work, some we met through DS preschool) - having children means, while you can't quite experience the city to the max in the same way, you will meet people regularly and easily. People give out their numbers regularly, it's very transient do everyone is keen to make connections.
Feel free to PM me if you want any more info! Would be lovely to have mumsnetter here!