Hi SanDiego,
Most Testing Centers follow a fairly standard procedure regarding the storage lockers.
Before going into the computer lab, you'll be assigned a locker (with a key). Everything goes in the locker: your food/drinks/cell phone, keys, wallet, watch, etc. In some cases, you might even be required to put your hat/coat (if you're wearing either) into the locker.
To be fair, you should NOT WANT to look at your cell phone on Test Day - you're at the Center to take the GMAT, so your focus should be on that task - so put your phone face down in the back of the locker. You can technically access your locker and its contents at any time during the Test, but you should plan to just briefly access it for your drinks/snacks during the two 8-minute breaks. All of your possessions will be safe while you are Testing.
GMAT assassins aren't born, they're made,
Rich