Japanese language schools in (or near) shinjuku?

It looks like in December of this year I will be traveling to attend a conference in Tokyo. They just announced that the conference will be in Shinjuku. 

I'm considering splurging and arriving a bit early and attending a language school. Does anyone know of any good language schools in or around Shinjuku?

I will be speaking at the conference. I'm on the fence with whether to go full-ninja-ganbatte and give the talk in Japanese. But regardless of whether I do or not, I still think it would be awesome to arrive early and take some private Japanese lessons.

I can definitely look for this info myself online. I just thought getting some feedback from real people on their experiences might be helpful!
Edited: 2017-09-11, 12:54 pm
I think most of the schools will arrange private lessons. But private lessons will be cheaper if you can coordinate with a person to meet for language class in a cafe. And 100% focused on you.

My friends studied at Nichibei in Yotsuya and liked the emphasis on speaking and listening vs. kanji study; that school was affilitated with Oberlin College. A few other friends liked ARC quite a bit and you will see a lot of comments on the internet about this school. KCP is probably the largest language school in Japan. Kai is smaller and my friends thought it was fine.

Also I sense the language school model has reduced focus on westerners and heavily towards Chinese & Koreans wishing to enroll in Japanese universities or trade schools. But each school seems to have a slightly different bend.

Rates may be significantly lower if you enroll directly via the school vs. a third-party or your local university.