Turn off all connectivity except GPS
Solution 1:
If you want to completely disable all cellular abilities (calls, texting, data) you could simply take out the SIM. True GPS still works fine, as that does not use the cellular network.
Solution 2:
You can go to Settings and turn Cellular Data off (turn WiFi off for good measure also in case you wander past a WiFi network). Also turn on Do Not Disturb mode. You still use the cell radio to locate your position, unlike in Airplane Mode.