Kilburn / Sth Hampstead / Brondesbury is NW6 (All Zone 2)
Regents Park, Camden, Marylebone is NW1 (Zone 2 & 1)
From Kilburn to Imperial in Sth Kensington should be about 35 minutes as Zaf stated. 2 lines from Jubilee to Baker Street and Circle to Sth Kensington.
As for area - If your talking about actual Kilburn, just watch yourself especially roads off the high street. I know someone who works in the post office base their and it has been robbed countless amounts of times - all early morning or late night of course.
I think you should look out more in this area than most others for example. Sth Hampstead is OK, and Brondesbury should be just abouts alright.
NW1 - Most of NW1 is lovely especially Marylebone, Regents Park - in fact richest residence in UK was based in Regents Park at one time. Not sure about now.
Camden Town is a grungy young area with worries only reserved to canal side acivities at the night time. No worries at all during the day. You do get loads of drug offers, but this is standard in Camden and no real worry should be made.
NW5 - Kentish Town (Zone 2) - the residential side to Camden Town. Bit of a dive and a dull area IMO. Warden Road is a prime example of this. Its in the middle of a formed estate that lies off of Malden Road where another of my good friend lives. I personally wouldn't walk from Malden Road through to Kentish Town Thameslink station at night. I just feel there are definetly safer areas than this! But I guess if there are loads of students there that I didn't know about, they would have a better idea than me.
Last time I walked through that hell hole of an estate, we got stares. We are not exactly the smallest of people either . . ..