Interesting topic. I used to ride through "bad" areas of Atlanta after getting out of work at 2 or 3AM. And then bike to my house in a "bad" area. My only weapon would have been sprinting, or my U-Lock. I rode in downtown Los Angeles after hours too. Worked at 9th and Gladys, a rather scary spot, and lived at 7th & Normandy. I've ridden through the Tenderloin and Mission district in SF many a late night/morning, etc. To me, it's all in people's heads (not a bad thing), i.e., their perception. Are you safer carrying a weapon like a pistol? I dunno. There are a lot of what-ifs involved here.

What if you pull your pistol in self-defense? Now the next time you ride through there you are "the guy on the bike with the pistol" ... a marked man, so to speak.
What if you ride through there 3 times a day for 10 years and never needed to carry it? Seems like a waste of energy to me. The resources that could have been used in the quest for personal protection could have been put towards a more selfless way.
What if .... What if .... What if ...
If you think you need one, and you really want one, and you can get one, and carry one legally, and it is one of your rights, then by all means make the choice. There's no one in here that can decide for you. Your world through your perception is just that.

As for me, a simple nod of the head or just keeping my eyes on the road always got me by. I was always another vehicle just passing through. I'll add my agreement that riding "around" an area is always an option. Those of you that think otherwise are, well, wrong. Good luck with your decision and your ride[s].