My obinion about best asian navy, should be some sort of tie between japan, china and india. Of these its pretty hard to rank them, couse it depends on lot what part you want to embhasis. China has nuclear submarines, a key feature of world class navy and when the 094 class is fielded, an ocean going nuclear deterence that buts china finally on par whit US, Russia, UK and france. India has carrier and good tradition of using them as well as secured future to operate them. Japan in other hand has well balnced conventional escort force with out any strategic reaches, thougth climpses of acuiring one.
Wheter Russia is to considered as Asian nation, remains more of political question. Nevertheless Russian's sole elements still keeping it at the top of the naval legue arent based on Asia, but in Europe. USN have strong precence in Asia, but isent asian nation
south Korea has single LPH, few licence build german diesel subs and upcoming Aegis ships....Its rather silly to but it above India or China as its large surface combatant count doesent reach over ten at this moment.