Hi Christine,
That is a very good question. I live in Paco in PaP and I feel safe. I run a lot of my errands by foot, sometimes walking for 20-60 minutes to go and come back. When I first moved here about 10 weeks ago I was quite overwhelmed by everything. Traffic is a little crazy and can be dangerous if you are not paying attention to where you are walking.
However, I do feel safe walking around during sunlight. No one really bothers me... I would not advise any woman to walk alone at night though but that is just common sense. I would avoid walking alone at night back home too. Being a foreigner, you should always be that much more cautious.
I also work a quater of the time in the South and I must admit that I feel a lot more at ease, relax and safe there than I do here in PaP. That is mainly because there is less traffic and everyone knows each other in smaller villages so there is this social community incentive to not cause any issues (that's my impression anyways).
Cheers!