Despite very efficient superconducting nanowire single-photon detectors (SNSPDs) reported recently, combining their other performance advantages such as high speed and ultralow timing jitter in a single device still remains challenging. In this work, we present a perfect absorber model and the corresponding detector design based on a micrometer-long NbN nanowire integrated with a 2D photonic crystal cavity of ultrasmall mode volume, which promises simultaneous achievement of near-unity absorption, gigahertz counting rates, and broadband optical response with a 3 dB bandwidth of 71 nm. Compared to previous stand-alone meandered and waveguide-integrated SNSPDs, this perfect absorber design addresses the trade space in size, efficiency, speed, and bandwidth for realizing large on-chip single-photon detector arrays.