No, I don't think it's crazy at all.
I don't think it would be crazy for me (a single guy) to do the same sort of trip, provided employment and financial and other mundane details cooperated, and I don't see any reason why it should be different for a woman rather than a man. There certainly are some neighborhoods where one would not want to be, whether man or woman, armed or unarmed; but the best solution is to avoid those neighborhoods if possible and basically just exercise a bit of common sense.
This time of year, I think it not the least bit crazy to prefer to be someplace more southern than New York!