A non-Asian friend of mine just returned and said that it felt fine for security. He complained of getting hit up by desperate touts, especially in Ubud, which is a shame.

For calibration, he plans to take a motorcycle trip solo from Singapore to Cambodia, so what he considers secure may vary from your definition.

I'd take my family there, but would avoid the Kuta area and Nusa Dua (which I avoid anyway).
Rich