I usually just sneak straight through Quarry Junction right after leaving Doc Mitchell's and run past the guards at Camp McCarran to take the monorail to the Strip. When you start a new playthrough of New Vegas, where do you go after leaving Goodsprings and why?
I sprint through Quarry Junction, going through a rocky area where aggro’d deathclaws that are inevitably chasing me will have pathfinding problems and get stuck.
I generally follow the quest line to the Strip so I'm high enough level by the time I get to it. I really like Cass so I make it a priority to get her as a companion as early as possible too.
I buy as much dynamite as I can from Chet and then climb up the hillside by the cazador road. You can perch yourself safely above the cazadors in the abandoned campsite and blow them to bits/shoot them without fear. Then I grab my free fireaxe/chance's knife and run towards Red Rock and through the fiends collecting heads on my way. It's relatively safe and great for exp farming with the big horners, geckos, and fiends (and Bonnie Springs if you're feeling spicy).