问题:

Would it be possible to take the ip address of a wireless router that an android phone would connect to and determine in the app the relative location of the ip?

回答1:

There's lots of online APIs available to determine a location based on an IP address, e.g. here, here, or here.
You could make a request to one of those services, passing in the appropriate "Internet-facing" IP address (which is different than the internal IP address that usually starts with 192.168., see here for an explanation).

回答2:

if your goal is to get the user's location, use android location services. if your app has requested it and the user hasn't disabled wireless location services, it will use wifi as well cellular networks. it's already packaged right into the SDK and convenient to use.

it might not be a nice thing to go behind the user's back with other methods and get their location without requesting a permission to do so. if you need their location, you might as well go through the approved mechanism.