In this paper, a delay-angle information spoofing (DAIS) strategy is proposed to enhance the location privacy at the physical layer. More precisely, the location-relevant delays and angles are artificially shifted without the aid of channel state information (CSI) at the transmitter, such that the location perceived by the eavesdropper is incorrect and distinct from the true one. By leveraging the intrinsic structure of the wireless channel, a precoder is designed to achieve DAIS while the legitimate localizer can remove the obfuscation via securely receiving a modest amount of information, i.e., the delay-angle shifts. A lower bound on eavesdropper's localization error is derived, revealing that location privacy is enhanced not only due to estimation error, but also by the geometric mismatch introduced by DAIS. Furthermore, the lower bound is explicitly expressed as a function of the delay-angle shifts, characterizing performance trends and providing the appropriate design of these shift parameters. The statistical hardness of maliciously inferring the delay-angle shifts by a single-antenna eavesdropper as well as the challenges for a multi-antenna eavesdropper are investigated to assess the robustness of the proposed DAIS strategy. Numerical results show that the proposed DAIS strategy results in more than 15 dB performance degradation for the eavesdropper as compared with that for the legitimate localizer at high signal-to-noise ratios, and provides more effective location-privacy enhancement than the prior art.