Best way IMHO is to study by yourself. It's the most efficient way and you can study what you want and don't get a forced confrontation with old and outdated methods or materials. The Mandarin spoken in Beijing is (again IMHO) very good. It's clean and well pronounced and way better then i.e. Shanghai. But I guess that may count for other NE cities too, Tianjin, Dalian, Changchun etc. Cost of living in those cities might be lower then in BJ. But BJ will have way more distraction, which can be an advantage, or disadvantage at time.

Beijing Language University i have an american brother (not really relative). i used to teach him chinese online.. now he comes to china and studies in that university, getting huge improvement!! so i strongly recommend you to study there...ohhh plus i have a friend from Belgium, he just arrived at Beijing, and decided to study there ... so go for it :) wish you good luck dude

北京语言大学 or BLCU is a good school. At least it's formal and official.

I would advise you not to go to Beijing. Beijing has far too many English speakers who are going to constantly want to use English with you because you have white skin. My advice is to go to a mid sized city somewhere far away from the mega cities. I say this because you will be forced to speak Chinese every single day in order to survive daily life. That's how you really learn a language. That's also what I did, and now my Chinese is really quite excellent. Just search for some universities that offer Chinese language programs, they will tell you the price for the course, boarding, and so on. I paid 14,000 RMB for a 6 month program, including all expenses, and to this day I still think it was one of the best decisions I ever made.

你在北京吗？