Proximity detection with rfid
RFID would require quite high gain antenna to work at that distance, but it's certainly not impossible. RFID is not designed to work at that distance, as passive tag gets the power over air. There would also be problems of interference if multiple RFID-tags would receive the signal.

My first thought is to use pair of smartphones for the proximity detection. You could use one phone's WiFi to scan nearby APs and detect if the other phone comes in range. With the signal strength, you can approximate how far the other phone is.

You also could fo this with other RF-chips and Arduino Yun. For example, you could use pair of nRF24L01+ (it's cheap and there's a lot of examples available), one connected to Yun and another to another microprocessor. Configuring the second one as ping-back node, you could measure the distance by sending ping-packet from Yun and measuring the time it takes to get an answer from the other node. This solution also enables monitoring distance to multiple targets.