You really have to look at all of Los Angeles as the "neighborhood" for USC. The campus is very nice, as I mentioned, the on campus housing is very limited and USC has a very large "commuter" population. the Greek system is pretty strong and other than football game days, the "greeks" provide alot of the "social scene" at the school.
The immediate neighborhood around SC is not dramatically unsafe, but you'd best not venture too far away, especially at night. There is a big revitalization going on around USC. Just north of Campus is the Staples Center (lakers/Clippers, etc.) and immediatley adjacant to campus is the new Galen event center for uSC basketball, volleyball, concerts etc. Both border on Figueroa Avenue and efforts are being made to make sort of a sports/entertainment/hotel corridor on Figueroa from Staples to USC and hopefully to add housing, but that's just all starting or in planning/hoping stage.
I think as an SC student you're going to find most of your fun and activities traveling around Los Angeles/SoCal. There are certainly events on campus, sports, theatre etc. but, again, with limited on campus housing there is not a huge community type feel and weekends, other than football weekends can get pretty quiet around school.
I went to USC MANY moons ago. Academic standards are much higher (I doubt that they'd have me now), but I don't think things in general have changed alot. Again, pretty big greek system presence, limited on campus housing and limited around campus and students live immediatley next to campus or, if not, then they are all over LA and thus a pretty big commuter presence.
My personal taste is more of a college town type atmosphere, which isn't LA, but being from here I don't have the same perspective of someone from out of the area who may well find a figurative (and literal) Disneyland out of all that LA has to offer.
At the bottomline I wouldn't be scared off by the "reputation" of it being in a tough neighborhood. There's no reason for students to be in these "rougher" areas, there are no attractions of any sort there and USC does strive to keep good relations, participate in community activities, help with building parks, tutoring at schools, etc. and the campus itself, fraternity row, etc. are extremely safe.
Most of my kid's friends that are now students there like it alot, I don't think by small coincidence all of 'em are in fraternities/sororities, which if you are from out of state/out of SoCal, I think is very helpful/beneficial.
Bottomline, definitely a school to consider. Professional schools are tremendous as are most undgergrad departments and SC alumni network is amazing. And you get the horse mascot and all those Rose Bowl games to boot.