The Billy Bar is located directly behind NoobsNoobsNoobs, you can easily access it by going through the back door of the Pawn Shop, avoiding the long walk around the block. The bar has great missions for new players, rewarding you with a free weapon as well as directing you towards the Beer Garden, and a free vehicle to help you get there! There is also a completly free instance here, this bar is great for new or non depositing players and I highly recommend you check it out.
The bartender will start the mission and hire you to work at the bar if you can get her some much needed alcohol for her patrons. Sadly the only source of alcohol is protected by avatars at a PvP area known as the Beer Garden, so she needs you to go there and get some for her. After recommending you grab a vehicle from the pawn shop for basically free, she marks the Beer Garden on your map and you are on your way. She will have more work for you at the bar once you get her the Kegs.
There is an angry patron who gets mad if you touch his drink. Touching his drink will start a free instance, it’s a great chance to experience your first instance, and at no cost or risk. When you touch his drink he will call all of his Forum Troll buddies over and trash the bar in a big bar fight with you. Each one has 3 HP and about 25 of them spawn, they are quite easy to take out.
After you are done, rob the cash register and you will be returned to a nice clean bar. I can only assume the bartender comes back from her lunch break and cleans up quickly, not caring that you robbed her register, it’s payment for getting rid of all the trolls.