i know a very famous song, two tigers

苏打绿 - 小情歌 Hope this help!

aw, my god, Chaney!

I don't know chinese at all but that song sounds so fragile and tender I just want to cry Q_Q

I also recommend a song from 邓丽君，《我只在乎你》。

here is the link i find in youtube: https://www.youtube.com/watch?v=N72dsXD2GdM

The songs are quite old, and therefore there are quite a lot of fans.

Besides the songs,  when you talk about 邓丽君，you could always find topics with other people. The singer, 邓丽君 is some kind of the symble of the past time. :-)

I know 5 or 6 songs suitable for intermediate learners, however I will just highlight 2 of them, give it a try.

Teresa Teng (邓丽君) - 月亮我的心 - The moon represents my heart (Despite not being modern, everyone know this song and it is a huge classic. The lyrics and the characters are easy and besides that the music pace is quite slow, which make it easy for begginers.

周華健 - 朋友 - Friend (ship) Once again, another classic. Not so easy as the previous one but still on the intermediate level.

Cheers