The title pretty much says it all. Group questing really only seems to net me 10 - 15 social points a conversation. What's the best way to quickly level up my social points?
The best way to quickly level social points is to repeatedly run the first flashpoint in the game (The Black Talon/The Esseles) with a group of four people. The conversation density is incredibly high here, and there are a large number of conversation options to earn Social Points from. Even better, if you significantly outlevel the instance, you can blast through the whole thing in a matter of minutes. This is also a great way to make large-scale alignment shifts should you need to for some reason late in the game.
As for how to get a group of four to do this? Just advertise in Fleet General that you'll happily run people through, or bring along three friends alts. You'll be doing them a huge favor getting them some easy XP and gear, and you'll rake in the social and LS/DS points.
I just ran through Black Talon a few times with another player (we're both level 50). Took us around 20 minutes and gave us roughly 100 Social Points each, though it would obviously be more if we had 4 people. We also got 200 Light/Dark side points, which can be helpful if you're short on those as well.