i live in hammersmith. tube station is ok, there are drunks and annoying kids that hang around there, but it's not that bad. i think you have been misinformed. there are a lot worse places to live.
i've heard a lot of people have got mugged around charing cross area - greyhound road. so personally i would never live that way. i think it's too far away from teh tube station, and i hate fulham palace road. but i am really picky. lots and lots of people from imperial live that way and in fulham and have no problems. i'd personally prefer to live the other side of the station, which is where i live now.
i wouldn't live in shepard's bush either, i dont think it's very safe.
i guess imp would have no problem with helping you find accomadation but normally landlords don't advertise until about a couple month before their places are ready, so you don't need to look until the summer. imp's help isn't very good in my opinion. they do have lists of landlords they are affiliated with, but there are mixed views of the conditions of these places and the lists are normally outdated. most people go through estate agents.
people normally live around hammersmith, fulham, paddington, bayswater, gloucester road, earls court etc etc. there are bad and good areas in all these places. - eek i know that's not particularly helpful. i think you have to go house hunting and see for yourself too - if it's near a housing estate, far away from teh tube station going down quiet streets etcetc
it also depends on how much you are willing to spend.
i hope i've helped some. feel free to ask me any questions.
xxxx