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This paper studies UAV path planning in areas where GPS signals are not present. Because these drones can easily get lost when they don't have GPS, they must rely on dead reckoning and occasionally pass near cellular towers, which act as landmarks to reset and fix their position. The goal is to find the shortest path from a start to a goal location while keeping the estimation uncertainty within a given bound. To solve this problem, we propose a localization-constrained A* planner that treats uncertainty as a hard constraint during search. The robot state and covariance are propagated using an Extended Kalman Filter (EKF), and only paths that satisfy the covariance limit are considered. We also show that the proposed method does not affect heuristic used in A* and remains admissible and consistent, ensuring optimality among all feasible paths. Extensive Monte Carlo simulations and PyBullet quadrotor test show that the proposed method finds shorter and more reliable paths compared to RRT* and PRM, while always satisfying the uncertainty constraint.