Someday I really enjoy going to the bar and chilling along with the company of the live bands, but it always ended up disappointing me as most of the bands only sing rock and pop. I'm looking for bar that has band that perform music like Lana Del Rey's and Enya's,music that can bring ones to another world (excuse my exaggerated description but that's how I feel every time listening to their music ) Please list down any bar you know that performs this kind of music. TIA

This old piece may partly answer your question. There's several of similarly toned write ups over the years but in general this is the hard reality especially here in Malaysia where musical appreciation are heavily "time sensitive" (read:- trend based) and narrowly scoped.

Not really a cafe/bar but you can try Merdekarya.

I'd suggest finding bands / musicians that play the music you like, and follow them rather than relying on a venue.