The "property" actuator on it's own only senses the value of a property. This is useful if you want to make sure something is at a certain value (i.e. Money = $250--> AND--> buy laptop) but it really has no direct sense of the physical world. The sensors that do are called the physics sensors.
Near: senses when a object is within a certain range.
Collision: senses if an object is being touched.
Radar: works like "Near" but not Omni-directional.
Ray: sends an invisible "beam", sense if something touches or obstructs the beam.
As you can probably see, the sensor you want to use is "Near", since it will sense if your player is near a certain object in the game.
Put the sensor on the object that you want to sense the player and set its property value to "player". play with the distance values till you get a result you like, make sure "reset" stay a tad higher than the "distance".