In cities like New York and San Francisco, once ground zero for the AIDS epidemic, the virus is no longer a death sentence, and rates of infection have plummeted. In fact, over the past several years, public-health officials have championed the idea that an AIDS-free generation could be within reach — even without a vaccine. But in certain pockets of the country, unknown to most Americans, H.I.V. is still ravaging communities at staggering rates.