since youre willing to pay Yen 250,000 per month for an apartment, i think you can find places within bike riding distance (10 - 15 minutes by bicycle) by any company.
Personally, I'd rather find a place 15 minute away by subway, and find a comparable place for 120,000 yen per month. Ive actually been looking into it myself, and found some decent one-bedroom apartments (called mansions in Japan) for 80,000 yen a month (which happens to be 20 minute subway ride from Ropponngi).
But then, ive been taking subways all my life, and feel comfortable with it. I'd go so far to say that 80% of the japanese take subways. Most companies in the city dont even allow commutes by cars.