Inscription at University for Chinese language program

Hi, I'm in Shanghai and I would like to subscribe to a Chinese language program.

What school/university is best appropriate?
Do I have to get out of China to get a student visa?

PS: My visa expires by the end of August, so it's quite urgent!

Nop,you can't get an X visa with an L visa in hand.
You have to go back to get a  temperary x visa with  letter of admission of a school in China.Then get an x visa in China which allows you to stay for half a year.
That's policy.