Japanese language school in Tokyo for these conditions?

Hello!

I tried looking up through this community and others for suggestions, but they all somehow miss my needs a little.

I am working in a profession that will allow me a relatively long vacation, and I decided to take that vacation from the end of July to the end of August for about 4 weeks (3 weeks August, 1 week July).

However, no language school seems to match this timeline exactly.

I am looking for places in Tokyo, preferably near somewhere really active like Shinjuku.

Cost isn’t a super big deal – I don’t want to go broke to do it, but I am willing to pay a premium for meeting these conditions.

The closest thing that met my needs was an academy called Lexis, but it is in Kobe.

As for my level, I am pretty much a beginner – I learned hiragana, katakana, and was able to have very basic conversation at one point. I can probably relearn it by the time I board the plane.

Thanks in advance!