I put mine in the oil pan above the drain plug; the casting is thickest there and it's still under fluid level. (Gen 1) Also, it's the bulk oil temperature; the value that most use when trading oil temperature information.
Don't know for sure, but often these is a threaded plug in the oil filter adapter assemby to close off where the oil passages were drilled. If you can unscrew the plug and install the pressure pick up there, that would measure oil temp just before or after the filter.
While the oil cooler lines are accessible, you wouldn't see any temps until oil ran through it (when the thermostat opened.) And on the return side, it'd be cooler than what's in the engine. Also, it would be in a pressurized location and another place to risk a leak.