Ultra-wideband (UWB) is considered the most promising radio technology for high-accuracy indoor localization because of its many desirable properties, including a sub-decimeter level ranging accuracy under line-of-sight (LOS) conditions, resilience to multipath fading, and low duty cycles. However, the accuracy of UWB localization deteriorates significantly in complex indoor environments due to the presence of non-light-of-sight (NLOS) propagation that may introduce a considerable positive bias in range measurements. In this paper, we present a localization method that improves the accuracy of UWB localization in mixed LOS/NLOS indoor environments by using multiple localization algorithms optimized for different localization scenarios distinguished by the number of LOS-measured distances. The method adopts a fingerprinting-based algorithm to obtain location results under NLOS-only conditions and uses the conventional multilateration algorithm when at least three LOS-measured distances are available. Additionally, the algorithm set includes two novel hybrid localization algorithms for scenarios with one or two LOS distances. These algorithms use the LOS-measured distances to limit geometrically possible locations and then employ fingerprinting to perform the final location selection. We test our approach in a realistic indoor environment over numerous experimental scenarios. The experimental results show that the proposed localization strategy reduces the mean distance error by 3 to 20 cm compared with the traditional fingerprinting-based approach.