This passage is from The Children's Bach by Helen Garner
He would have liked to move around her house and examine all its icons, or to hang over the front windowsill with her and make remarks about the dress and gait of passing pedestrians; but he wanted also to get her outside and on to his own turf, into public places where no-one was host and no-one guest, where everything had a price, where he could get what he wanted, pay for it, and keep moving in long, effortless, curving afternoons unsnagged by obligation or haste: the idea of destination meant almost as little to him as it did to Billy.
Is "curving afternoons" used metaphorically, and means afternoons that you feel relaxed?
Does "the idea of destination meant almost as little to him as it did to Billy." mean: He had not got any idea about destination and he kept walking and where ever was his destination?
And I think "turf" here mean the places that he went in his free time. Am I right?