Alright, so I've done some thinking on this, and some exploratory searching. From what I can tell, using signal strength to determine range is possible, but Not Easy.
So I had another thought.
I have an HC-SR04 ultrasonic rangefinding device. It has an accuracy of 3mm (On best of days, of course). Sends out a ping, listens for the ping to return, checks the time. Does math, then finds the distance.
I feel this could be utilized to work for what I want. The "Base" device would have a set of (preferably omnidirectional instead of the HC-SR04's directional) three ultrasonic "senders." Placing them a decent distance apart - A centimeter or two should suffice. You'd have some form of wireless transmitter/receiver as well. This would let it pair with one (or more) pretty simple wireless devices. Those devices would essentially just be an ultrasonic receiver plugged in to a wireless transmitter/receiver.
The "Base" would periodically send out pulses, sequentially, from its ultrasonic senders. This would involve transmitting a radio signal saying "Hey, I'm sending the signal" - Then after a predetermined time period (To let the unit "prepare" for the incoming signal), it would send the ultrasonic pulse. The receiver would then mark down when it received the signal, and the delay between the "I'm sending the signal" message and the actual receipt of the ultrasonic ping. Take out the programmed delay, and you then have the travel time between the base and the item, and thus the distance. Instead of having three separate "I'm sending the signal" bits, it could be just "I'm sending the signal" and then after, say, a 0.25 second delay, send the first pulse, another .25 second delay, the second pulse, and another .25 second delay, and the third pulse.
Then the receiver would mark when it received the first, second, and third pulses and send that time information back. Math would give the distances for the first, second, and third transmitters, and more math and fancy code would give an X,Y location (Relative to the base unit).
Is this feasible? It SOUNDS good to me, but... Who knows. I'm also not sure what sort of equipment is available - I know there's wireless connectors, but omnidirectional ultrasonic devices? No clue.