I think you misunderstand what I'm saying in response to you meeting a lot of Libertarians in a Liberal city.
Libertarians and Liberals both dislike regulation on one's personal matters, so they share that social view. Young people are increasingly cynical of our government/current representation, which would naturally push them towards small government ideals. Combine liberal social views + government cynicism, you get libertarianism. Your experiences make sense.
I agree, and I think the minimum should be set in each county, vs an unrealistically high federal wage.
As far as LA, I don't know what it takes out there to provide for yourself. But as I've said in another thread, I do believe places where the cost of living is high, the minimum wage should be higher. $10/hr in LA or NYC gets a lot less than $10/hr in Alabama.
And yes, I know the response is "Well, just move" (which I agree to disagree on)... but I just wanted to clarify that I don't think some lofty amount should be the minimum wage universally.
As far as healthcare goes, I support a single payer option for all legal residents.