We introduce JetViT, a novel family of hybrid-architecture Vision Transformer (ViT) models that match the accuracy of state-of-the-art full-attention vision foundation models while achieving substantially higher inference efficiency on high-resolution images. At the core of our approach is Post-Training Attention Search, a post-training acceleration framework that converts pre-trained full-attention ViTs into efficient hybrid-attention variants by identifying and replacing redundant full-attention blocks with linear or window-attention blocks. By inheriting the MLP and attention weights from the base model, Post-Training Attention Search efficiently explores the architectural design space through three key steps: (1) optimizing the linear-attention block design; (2) finding the best combination of linear-attention and window-attention blocks; and (3) identifying and preserving critical full-attention blocks. We evaluate JetViT on two representative high-resolution vision foundation models, DINOv3 and DepthAnythingV2. On the NVIDIA H100 GPU, JetViT achieves up to 1.79x higher throughput and up to 44.81% lower latency without sacrificing accuracy. We will release our code and accelerated ViT models soon.