I think Korra was crying in the end because maybe she wasn't sure of her decisions, maybe she does not believe in leaders and maybe some part of her agreed with Zaheer that restoring balance making everyone equal is right.Sure Korra does not want chaos but she was talking to Zuko getting info about Aang and wanted advice what Aang would do, since Aang was a air nomad he had been told to not use violence against anyone, only when attacked yourself. To me the Republic city president looked fishy in the last ep, like he has plans with Korra, just something about him does not feel right. Or maybe those were happiness tears expressing the relief, freeing her from avatar duties or the end of fighting?