Look into lower Westchester county. You're not going to be able to afford a house on that budget, but you could probably get a co-op with 2 or 3 brs.
The reason I reccomend Westchester is because it has an unusually large Japanese population. On the whole it isn't that big, but Westchester basically has the most Japanese people (per capita) on the entire East Coast. This is largely due to Keio University operating a Japanese High School on the edge of Manhattanville college's campus over in Purchase.
Keio Academy of New York > Home
In White Plains they have Daido supermarket (
Home), which I believe is the largest Japanese market in Westchester. There is also an attached sushi bar that is supposed to be really good, got written up in the NY Times last year (
DINING/WHITE PLAINS; Authentic and Exciting, Right Down to the Soy Sauce - New York Times)
There is also a concentration of Japanese stores in Hartsdale around the intersection of Central Park Ave & Hartsdale Ave. There is a Japanese Market, a Sake shop, a Japanese bookstore, a Japanese language center/social club, a Japanese restaurant (run by Japanese people, not a Korean joint), and there is also a pretty good sushi restaurant in Hartsdale itself (I think the name is Azuma).
In Scarsdale there is a Japanese market and a Japanese deli/sushi type place on 22.
In Tuckahoe there is a Japanese language church:
New York Japanese Church.
I'm sure you guys already know about Mitsua in Edgewater, NJ. That place is the largest Japanese supermarket in the NYC area. It also has a pretty good food court. If you go on the weekends go early because its hard to find a parking spot for most of the day.
There are a bunch of other places scattered throughout the area. PM me if you need anymore details.