In cluttered scenes with inevitable occlusions and incomplete observations, selecting informative viewpoints is essential for building a reliable representation. In this context, 3D Gaussian Splatting (3DGS) offers a distinct advantage, as it can explicitly guide the selection of subsequent viewpoints and then refine the representation with new observations. However, existing approaches rely solely on geometric cues, neglect manipulation-relevant semantics, and tend to prioritize exploitation over exploration. To tackle these limitations, we introduce an instance-aware Next Best View (NBV) policy that prioritizes underexplored regions by leveraging object features. Specifically, our object-aware 3DGS distills instancelevel information into one-hot object vectors, which are used to compute confidence-weighted information gain that guides the identification of regions associated with erroneous and uncertain Gaussians. Furthermore, our method can be easily adapted to an object-centric NBV, which focuses view selection on a target object, thereby improving reconstruction robustness to object placement. Experiments demonstrate that our NBV policy reduces depth error by up to 77.14% on the synthetic dataset and 34.10% on the real-world GraspNet dataset compared to baselines. Moreover, compared to targeting the entire scene, performing NBV on a specific object yields an additional reduction of 25.60% in depth error for that object. We further validate the effectiveness of our approach through real-world robotic manipulation tasks.