If we're talking uni halls, there's nothing that directly serves King's unfortunately, so I'd advise not applying for anything north of the Royal Mile. There's a good selection around Newington but they are quite popular. I stayed at Hermit's Croft last year and the cycling commute wasn't too bad once you got used to the hills. As for buses, there's a million and one routes going south towards Cameron Toll. Best of luck with your applicationa and exams, let me know if there's anything else you specifically want to know, I am in my second year of Physics at UoE.