Hi. What's your level? Can you read hanzi?
This drama is for learners, but they speak FAST and in a natural way: 快乐汉语。It has hardcoded Chinese and English subs.
https://www.youtube.com/watch?v=svdnzVJ9KA4&list=PLdT5MUO4gYEdQBMFtkF5g803FJZOss-ip
You can find dramas with Chinese subtitles on Huace's global fun YouTube channel. In Netflix, you can also find "A love so beautiful". It's also on YouTube if you search for the Chinese name, 致我们单纯的小美好.
However, the one drama that seems to be amazingly popular is "Ode to Joy" or 欢乐颂. You can find it here. It has hardcoded Chinese subs and soft English subs:
As for songs, my favorites are:
对不起我的中文不好
我不想念
对面的女孩
小苹果
许巍 - 我的爱 、蓝莲花、 曾经的你
这三首歌强烈推荐