The wire won't run up the wall unless it's running from the breaker to another room above. Even then, the odds are very low. 20yrs of handyman and diy projects has taught me that. I've never hit a wire.

The recep boxes are attached to studs. The stud will be on either side of the recep box. Tap next to the plug and one side will sound solid (stud) while the other will sound hollow and get deeper as you move away from the stud. You may even be able to see the stud by taking off the recep cover of the drywall hole is big enough.