Location aware applications that provide smart city building blocks are growing in popularity as mobile devices approach ubiquity. While the specific definition of "smart city" is still evolving, most agree that the term implies integrating communication and information technology to advance quality of life. Location-aware mobiles apps can provide many services tailored to a user's current location. Several current apps provide routing and proximity alerts for hazards, but require users to disclose locations and data owners/providers (DO) to advertise areas of interest locations. We analyze three encryption based approaches that provide granular proximity detection without openly divulging any location information. These approaches use different techniques to assure the user and DO mutual privacy while still providing proximity detection of users to defined areas of interest. We implemented the approaches, and as part of our implementation effort, extended the functionality of one of the approaches, originally designed as a generic Secure k-Nearest Neighbor approach, to align it to our specific problem domain. We compare the security and privacy guarantees, and the efficiency and accuracy of each approach. Our results can be used to choose the most applicable mutually private proximity detection (MPPD) approach for a smart city environment.