Ok, so I need to get Esbern's location from Brynjolf, and I can't persuade him to give it up. I have 47 Speech (37+Mask of Clavicus Vile) and I can't persuade him.
Doing Brynjolf's quest is not an option for me. I am not joining the Thieves Guild. Brand-Shei is my friend, I am not going to place the stolen ring on him.

go to get the ring but get caught so don't sneak then he will tell you after you get caught.

You don't even have to get caught. Just stand there and let him finish his speech and he'll still let you join.

No, I don't want to join the Thieves guild, I want to get Esbern's location out of Brynjolf, but I can't persuade him. I am not doing his quest, Brand-Shei is my friend.
I need to know how high my Speech skill needs to be to persuade him to tell me Esberns's location. It is currently at 47.

I got Esbern's location without ever talking to him so ask around in the inns and you should be told where to go.