Scout the eight sectors around Gecko and return to Stark

Once you can enter Vault City, head to the Corrections Center and talk to Sergeant "That's SERGEANT to you" Stark. Mention patrols to him and He'll ask you to scout the area around Gecko. Quite a simple mission and a good payout for what need to be done. Return to him afterwards for your reward.

You'll need to physically move your character around Gecko on the world map and visit each of the eight squares that surround it. If you miss one, you won't complete the quest.

Reward:
 * 350 Experience points
 * $300