A lot of LA gang members moved to Vegas, too. Notice Vegas's crime increased in the time LA's decreased.
When cities "get rid of crime", nearby cities pay. They inherit the crime. It's that simple.
Someone mentioned this earlier in the thread in re: to the lowering of NYC's crime rate.
Another factor we aren't mentioning with the whole higher vs. lower rates in urban areas is gentrification.
Ex. where I am from Wash DC. The city as a whole was once the murder capital of America in addition to being the actual capital. Things really came to a head and finally improved when Marion Berry(who was strung out on coke and in bed with drug kingpins) was finally kicked out of office by the Feds. Allowing reformers like Anthony Williams and the head of the DC police Charles Ramsey to make drastic changes. Post 9/11 funding and the goverment contracting/tech boom did the rest. DC neighborhoods that I wouldn't have dared step foot in 25 years ago like Columbia Heights, U Street,H street are now lively places, and the murders/drug actvity has plummeted.
The big downside of this in DC(as well as other places like NYC, Boston, LA, etc) is that as the wealthy liberal white yuppies moved in and turned project styled housing into $1,500+(at a min) "luxury" apartments , yoga studios, craft brew bars etc. This has forced large numbers of low income people into neighborhing areas like Pringe Georges and Charles County Maryland. And even into places as far away as the West Virginia Panhandle and Pennsylvania. Inevitably some of the crime has followed and even clashed with existing elements in these places too.
Same thing goes for NYC, LA, etc. Ex. New York gangs have popped up in PA's Leigh Valley and LA ones have set up shop in Stockton.