That's the key, you need the MAC address of the embedded WiFi NIC on the stolen item, which should be on box that your laptop came in (I think), or recorded on your wifi router (if it hasn't aged it out, or you've rebooted your router then its gone), or Apple tech support (but probably past level 1 tech support)
In my case, the app told me the Ipod was in a hospital, I assumed the waiting area, and used a program like to identify the person in the waiting rm. In your case, if the app directs you to a given area with 6 apartments, the moocherfinder app should be able to tell you which apartment.
This is essentially a 'two step dance', the "Find my Iphone" app gets you in the general area. Then, the link I gave you has an app called "moocher finder", which essentially tracks down a wireless MAC address based on its signal strength from a given laptop. There is an embedded video on the website with the guy using it, should be good watching.
You need to assemble a few things, should be cheap (less than $100, which assumes you have a spare laptop, or a friend who can temporarily donate one for this use) On the laptop you can download the Linux image on the website, and put it on a USB thumb drive, then boot off the thumb drive, that way you can run Linux w/out installing it on a given system.
You'll also need a compatible wireless NIC, there are some listed on the website. I bought a used one from Ebay, that way when I'm done I'll just relist it. The best NIC is one that can accept external antenna's, as the best way to locate is with a directional (Yagi) antenna. Below are two listing on Ebay.
Wireless Card
http://www.ebay.com/itm/Ubiquiti-SWX-SR71-WLAN-SR71X-802-11-a-b-g-n-300mW-Wirele ss-Card-MMCX-w-2-Ant-/230746485129?pt=COMP_EN_Routers&hash=item35b98ff189#ht_143 4wt_1185
Antenna
http://www.ebay.com/itm/16-dBi-2-4-GHz-Wifi-Yagi-Antenna-RP-SMA-Booster-16db-/30 0668395660?pt=LH_DefaultDomain_0&hash=item46013ba08c#ht_2073wt_952
Good luck.