I had a friend who stayed in a serviced flat right across the street from the front entrance of the Grand Hyatt Roppongi (and hence walking distance to your school). I don't remember the name, but it was about a block away from the Mori apartments, quite acceptable, and I am sure it was cheaper. Darn....with a search you can probably find it. Alternatively, you can take an Oakwood place for two weeks, arrive early, and search on arrival, although it is a bit riskier.