Looking for a hotel in $400 -$600 range per night in Tokyo near transit

Shangri-La Hotel, Tokyo

The Peninsula Tokyo

These hotels are very close to Tokyo Station.

The Tokyo Station Hotel is also worth considering:

1-9-1 Marunouchi Chiyoda-ku Tokyo, 100-0005

Hi,
You would definitely like The Capitol Hotel Tokyu in Nagata-cho, Chiyoda-ku, I Stay there when in Tokyo and it is exceptional. Superb service, great rooms and showers like you've never seen before. One of my favourites.
It is located atop 4 subway lines at Tameike-sanno / Kokkai-gijidomae station.
Nanboku Line, Chiyoda Line, Ginza Line and Marunouchi Line.
Hope this helps

This should be pretty easy with that price range. Tokyo Station has the Shangri-La Hotel, Tokyo, and the Marunouchi Hotel, and The Tokyo Station Hotel. I would choose Shangri-la of those three. Otherwise the The Peninsula Tokyo and Palace Hotel Tokyo are a quick 5 minute taxi or less and would be #2 &3. Those are all pretty close to. Mandarin Oriental Tokyo is close too but in a less convenient part. Otherwise, you can head to Grand Hyatt Tokyo or The Ritz-Carlton, Tokyo in roppongi.