Contrastive Language-Image Pre-training (CLIP) excels in global alignment with language but exhibits limited sensitivity to spatial information, leading to strong performance in zero-shot classification tasks but underperformance in tasks requiring precise spatial understanding. Recent approaches have introduced Region-Language Alignment (RLA) to enhance CLIP's performance in dense multimodal tasks by aligning regional visual representations with corresponding text inputs. However, we find that CLIP ViTs fine-tuned with RLA suffer from notable loss in spatial awareness, which is crucial for dense prediction tasks. To address this, we propose the Spatial Correlation Distillation (SCD) framework, which preserves CLIP's inherent spatial structure and mitigates above degradation. To further enhance spatial correlations, we introduce a lightweight Refiner that extracts refined correlations directly from CLIP before feeding them into SCD, based on an intriguring finding that CLIP naturally capture high-quality dense features. Together, these components form a robust distillation framework that enables CLIP ViTs to integrate both visual-language and visual-centric improvements, achieving state-of-the-art results across various open-vocabulary dense prediction benchmarks.