Some areas close to UCLA that you might want to consider are: Westwood, Brentwood, Mar Vista, Palms, Culver City, Beverly Hills, Bel Air, and Santa Monica.
Feel free to contact me if you have any other questions/concerns about the area.
You can always check with the Senior Lead Officer in the area of where you want to live or call the local police station, which for the UCLA area is the West LA Community Police Station. UCLA also has a Campus Police http://map.ais.ucla.edu/go/police who may also give you more information.
Most of the surrounding areas of UCLA are pretty nice...but you do need to check them out for yourself and make sure you feel comfortable in that area.
West Los Angeles
Feel free to contact me directly if you would like more information.
All the best,
Kat Becker, Realtor
Berkshire Hathaway HomeServices