In any big city in the US, there are dangerous areas that you should avoid at night.
For example, I just got back from Newark; I didn't want to wander around much after work because I didn't know the area. So, we took the PATH train into NYC, which I know well from having lived there.
You can walk around NYC at 2 in the morning---IF you know where to walk and where to not walk.
Similarly, there are areas of Houston I'd advise you to stay out of during the daytime. Most areas of Houston are fine 24/7; some are bad 24/7.
Just about anywhere, if you stick to the well-traveled, well-lit, "touristy" areas and keep a good eye out, you're fine. If you go wandering off alone---well, not a very good idea anywhere unless you know the area well.
Also, do not assume that the demographics you know from home apply somewhere else. Just because blacks and whites, whites and hispanics, hispanics and blacks, asians and whites, etc etc etc, whatever combination---just because they get along well in YOUR town does not mean that carries over to other towns. Blacks and whites (as groups) get along much better in Houston, for example, than they do in my old hometown of Little Rock.
Have fun in LA, one of my favorite places on earth. Nothing else like it. Sit on the beach under a palm tree drinking a bottle of good California red and watch the sun sink slowly into the Pacific.