Fallout New Vegas is better than Fallout 3 because it never forces you to kill a single thing to complete the game. It gives you so many nonviolent ways to level up your character that a Doctor Who run is totally, 100% feasible.
Tag Speech, Science, and Lockpicking.
Perks are Good Natured and Four Eyes.
PER 9 (10 with Four Eyes and a pair of glasses)
You are now equipped to lockpick, charm, and hack your way to getting to 100 speech, 100 science, 100 lockpick, and 100 medicine.