Deliver beer and booze (10 each) to Lydia.
Vault City's strict no-alcohol stance doesn't sit well with all of its citizens. Demand for genuine alcohol is high, and Lydia, owner of the Tap House by the Inner City main gate, is willing to fill that niche. She needs your help.
The job itself is simple: get ten bottles each of beer and booze, and deliver them to Lydia. The catch is getting by the gate guards, who search all non-Citizens entering the city. A good place to get all the booze and beer you need is NCR, the cantina tents to have 10+ of all possible drinks, so if you go to NCR you may get all the 20 bottles before going to Vault City.
If you've managed to become a citizen, or carry the false citizenship papers, then your job is simple: just carry the bottles through the gate. If not, then you will need to be creative.
There is a considerable delay between the gate's opening and closing. If you deposit your bottles on the hex immediately adjacent to the gate's track, you can retrieve them after you're searched. You may only be able to snitch a couple bottles at a time unless you can position yourself directly on the gate and prevent it from closing. Either way, you can eventually swipe enough bottles between gate cycles that you can collect all twenty for your delivery.