No data Map app

It uses a GPS chip, information from the location of WiFi sources and what's referred to as AGPS which, in general, is not as accurate and somewhat slower than what you would have otherwise. With data on, your accuracy and speed improves because you also use the Cell tower triangulation. (this is kind of a simplified answer and not entirely accurate, but it gives you the basic concept)

 

In airplane mode, everything is turned off, even GPS, read the support page here:

http://support.apple.com/kb/HT1355

Also, AGPS is not wifi triangulation. AGPS is assisted GPS which uses cell towers to speed the time it takes to get a GPS fix.

If what you want is to save battery and not use data, turn off Wifi and Bluetooth on the first page of settings, then go to General, cellular and turn off cellular data

 

I'm about 97% sure of that (gotta leave myself a little wiggle room )