That depends a lot on your salary and your standard of living, neither of which was clear in the post. If you're coming from a typical high-rent urban area, my guess would be that you can find a place for comparable rents -- but it will be half the total size. The reason is that *everything* is half-size here. The "execs" who insist on living in a 1500-sq-foot apartment with two baths pay through the nose because the only people looking for anything that size are execs with expense accounts. Supply and demand.

If you're stationed in your company's Yokohama office, you're looking to try your hand at living like a typical Japanese family of four would live, and you're not averse to riding 30-45 minutes by train each way, you can probably find something on your current salary if you had to. Yokohama and neighboring Kawasaki are full of areas where typical blue- and white-collar salarymen live.

However, since you have the opportunity to negotiate, see if you can get something like 200-300 thousand yen (2-3 thousand US dollars) per month for rent. Our family of four is living in Nakano for just over 200 thousand yen so it's gotta be possible to get lower than that in Yokohama. If they need someone here, that's probably pocket change for them.

Other than that, there's not much else to ask for. If you're not Japanese-fluent, try to get some language lessons thrown in. Nearly all Japanese salaried workers get their commutation expenses paid. If you're here temporarily, see if you can rent your furniture or, at the very least, get the company to handle that on both ends. It can often cost as much to *get rid* of things here as it did to buy them. And make sure the company will contact the realtor, pay the realty fees, and guarantee the rental. Those are the biggest pains associated with renting, after the rental price itself. And it's almost impossible to find anything reasonable outside of the realty network.