Field strength of radio signals is normally measure by a field strength meter.
http://en.wikipedia.org/wiki/Field_strength_meter Some of these devices are very broad banded and others are frequency specific.
A simple way to measure the FM signal strength at your location is to receive an FM radio signal on an FM radio that has something called an S-meter It measure the electric field in decibels and alternatively something called S -units
http://en.wikipedia.org/wiki/S_meter. An android device can not directly measure any of these, however some radios can do this with built-in S meters. An Android device is not an FM broadcast radio, however the phones do use FM signals. You already said that you do not want to measure the signals from a cell tower.
The trick is to make is sensitive on the specific broadcast frequency of the FM radio signal you are monitoring.
You might also Google use search terms like radio direction finding FM radio signal strength
Regards,
Steve