In Shibuya, under the bridge near the train station, many homeless people live under the bridge. They didn’t talk to me, but it’s quite an uncomfortable place to be in.
Some clubs in the city centre should be avoided. If people target you advertising their club, don’t go in. People have been known to be drugged and robbed.
The Red Light District is relatively safe in the earlier hours and if you’re with a large group of people, but avoid it late at night and if you’re intoxicated and there’s only one or two of you.
There are no real crime hotspots in the city, take extra care in busy tourist areas and apply the usual safety precautions. Watch out for quiet areas after dark and stay in the well lit main streets, and stay within the crowd.