I need to know the signal strength of a Bluetooth connection to a remote device that I make with my Android 2.1 phone. From the SDK, I can see that I can determine the RSSI
Sadly not for Android 2.1, but have a look at this API for level 18 (Android 4.3) which you could poll:
BluetoothGatt.readRemoteRssi()
Read the RSSI for a connected remote device.
See Android docs here