In this paper, we propose a unified localization framework (called UNILocPro) that integrates model-based localization and channel charting (CC) for mixed line-of-sight (LoS)/non-line-of-sight (NLoS) scenarios. Specifically, based on LoS/NLoS identification, an adaptive activation between the model-based and CC-based methods is conducted. Aiming for unsupervised learning, information obtained from the model-based method is utilized to train the CC model, where a pairwise distance loss (involving a new dissimilarity metric design), a triplet loss (if timestamps are available), a LoS-based loss, and an optimal transport (OT)-based loss are jointly employed such that the global geometry can be well preserved. To reduce the training complexity of UNILocPro, we propose a low-complexity implementation (called UNILoc), where the CC model is trained with self-generated labels produced by a single pre-training OT transformation, which avoids iterative Sinkhorn updates involved in the OT-based loss computation. Extensive numerical experiments demonstrate that the proposed unified frameworks achieve significantly improved positioning accuracy compared to both model-based and CC-based methods. Notably, UNILocPro with timestamps attains performance on par with fully-supervised fingerprinting despite operating without labelled training data. It is also shown that the low-complexity UNILoc can substantially reduce training complexity with only marginal performance degradation.