Sampling-based planning algorithms like Rapidly-exploring Random Tree (RRT) are versatile in solving path planning problems. RRT* offers asymptotic optimality but requires growing the tree uniformly over the free space, which leaves room for efficiency improvement. To accelerate convergence, rule-based informed approaches sample states in an admissible ellipsoidal subset of the space determined by the current path cost. Learning-based alternatives model the topology of the free space and infer the states close to the optimal path to guide planning. We propose Neural Informed RRT* to combine the strengths from both sides. We define point cloud representations of free states. We perform Neural Focus, which constrains the point cloud within the admissible ellipsoidal subset from Informed RRT*, and feeds into PointNet++ for refined guidance state inference. In addition, we introduce Neural Connect to build connectivity of the guidance state set and further boost performance in challenging planning problems. Our method surpasses previous works in path planning benchmarks while preserving probabilistic completeness and asymptotic optimality. We deploy our method on a mobile robot and demonstrate real world navigation around static obstacles and dynamic humans. Code is available at https://github.com/tedhuang96/nirrt_star.