People are funny - they wouldn't think twice about tipping $2 but they would balk at any cover charge and go somewhere else.

Rather than going for the low brow gigs maybe you should try going for the high brow ones instead. Restaurants in your area might be receptive to having some low-volume, high-quality music and $50/hour would not be unreasonable. Better than playing dives for half that amount. Rather than doing twangy Hank Williams stuff you could give it a more modern bluesy feel, like what Nora Jones did with a Hank tune on her first album. I think going for a classy approach and trying to appeal to an upscale market is a better option even if you're just singing and playing guitar.