Processing-in-memory (PIM) architecture has been proposed to accelerate state-of-the-art neuro-inspired algorithms, such as deep neural networks. In this article, we present PIMulator-NN, an event-driven, cross-level simulation framework for PIM-based neural network accelerators. By employing an event-driven simulation mechanism, PIMulator-NN is able to model architecture details and capture design details of the architecture. Moreover, we integrate the main-stream circuit-level simulation framework with PIMulator-NN to accurately simulate the area, latency, and energy consumption of analog computation units. To demonstrate the usage of PIMulator-NN, we implement several PIM designs with PIMulator-NN and perform detailed simulation. The simulation results show that memory access and interconnects make considerable impacts on system-level performance and energy. Note that such results are hard to be captured by conventional performance model-based estimations. We found some anti common-sense results while modeling the architecture details with PIMulator-NN. With several architecture templates, PIMulator-NN provides the users with a platform to build up their PIM architecture quickly. PIMulator-NN is able to capture the impacts of different design choices (e.g., dataflow, interconnect, data parallelism, etc.), and this could enable users to explore their design space efficiently.