Many phrases of subjective mood or sensation use a dative construction with "mir" in German whereas English uses different idioms:
Mir geht's gut. - I'm fine.
Mir gefällt das. - I like that.
Mir scheint... - It seems to me...
Er sieht mir aus wie... - To me, he looks like...
Das klingt mir nach... - To me, that sounds like...
Furthermore, you can say something along the lines:
Das klingt mir nach einem schönen Lied. - That sounds like a nice song to me.
Das klingt mir zu harsch. - That sounds too harsh to me.
Nonetheless, in your case no dative with "mir" is used. With a pure adjective, without "zu" (too) and without the noun the "that" is sounding like, there is no "mir":
Ich finde, das klingt gut./Das klingt gut! - That sounds good (to me).
Ich finde, das hört sich gut an. /Das hört sich gut an! - That sounds good (to me).
Instead of "sich anhören" and "klingen" in some parts of the German speaking world "tönen" is used; but as far as I know, no "mir" is used in a sentence like "Das tönt gut.", either.