We present UrbanFly: an uncertainty-aware real-time planning framework for quadrotor navigation in urban high-rise environments. A core aspect of UrbanFly is its ability to robustly plan directly on the sparse point clouds generated by a Monocular Visual Inertial SLAM (VINS) backend. It achieves this by using the sparse point clouds to build an uncertainty-integrated cuboid representation of the environment through a data-driven monocular plane segmentation network. Our chosen world model provides faster distance queries than the more common voxel-grid representation, and UrbanFly leverages this capability in two different ways leading to as many trajectory optimizers. The first optimizer uses a gradient-free cross-entropy method to compute trajectories that minimize collision probability and smoothness cost. Our second optimizer is a simplified version of the first and uses a sequential convex programming optimizer initialized based on probabilistic safety estimates on a set of randomly drawn trajectories. Both our trajectory optimizers are made computationally tractable and independent of the nature of underlying uncertainty by embedding the distribution of collision violations in Reproducing Kernel Hilbert Space. Empowered by the algorithmic innovation, UrbanFly outperforms competing baselines in metrics such as collision rate, trajectory length, etc., on a high fidelity AirSim simulator augmented with synthetic and real-world dataset scenes.