Visited KUL a number of times in the last few years. As a caucasian American, I 've never felt unsafe, and I concur with another poster that this extends to some non-tourist areas as well.

I usually stay in either the Bukit Bintang area, or near the junction of Jalan Sultan Ismail and Jalan P Ramlee near the Petronas Towers. The former location has a JW Marriott, Ritz Carlton, etc. while the latter has Shangri-La, Renaissance, and where I usually stay, the Concorde KL. The Concorde is immediately adjacent to a monorail station. Other hotels right nearby include Crowne Plaza, Equatorial, etc.

The new KL Hilton is another top property definitely worth looking at, and for many FTers coming in and out on their own on short trips, could well be the better choice. I'm usually in KUL for 3-4 night stays so it is less well-located for me, but no less a desirable property.

I usually stay near the Petronas Towers because Mrs. unagi1 likes to shop at the KLCC shopping mall right there.