Congratulations on your assignment. You'll both have an experience you'll never forget.
Atsugi I know well as I used to live near there and you can get to Yokohama and Tokyo fairly easily from there. Atsugi also is home to a US Navy air base.
With a yen480k stipend for housing you can live quite luxuriously in Atsugi and I don't know why you would rather live in Tokyo or Yokohama as housing will probably be 1/3 to double what you'd pay in or near Atsugi for the same thing. Besides, Atsugi is quite modern.
The commute to/from Yokohama station is approximately 40 minutes and you'd have to take a minumum of two trains depending on where you chose to live. Tokyo (Shinjuku) is also approximately 40 minutes and requires only one train and two or more depending on where you work or live.
Another consideration is the hectic rush hour commute in the mornings and evenings of which I am sure you will tire of after a few weeks and would probably wished you lived near your work in Atsugi.
Even though you would be given a vehicle by your company you will not desire to drive during rush hour either to/from Tokyo/Yokohama as the tolls and gasoline, is very expensive never mind the traffic. Instead, I'd recommend using your car for weekend or holiday getaways even though that will also be hectic at times.
Getting to Tokyo from Yokohama for your wife, if you decide to live there, is also approximately 30 - 40 minutes depending on where where she worked.
My advice, for what it's worth, would be to live near your work in Atsugi and your wife can commute from there. It would be alot easier on you and you could probably drive to work from your home as it would only be a short distance. You can get more house/condo for your yen in Atsugi also. Sure, you may enjoy living in Tokyo/Yokohama more, and with your stipend you can easily afford it, but the commute may not be worth it. But that's a choice you'd have to make.
I'd also opt for getting a place within walking distance of a train station. As Atsugi station is an express stop, you'll not have much difficulty getting to either Tokyo or Yokohama or the hot springs and resorts to the south of Atsugi from the Odakyu train line that serves Atsugi.
Also, since you and your wife are getting a week to house hunt and such, that's great! Take the commute yourself to Yokohama and Tokyo and compare prices, time, hassle, etc. I think you'll probably find living in Atsugi to be your best bet even though your wife may have to commute an hour or so by train to Tokyo if/when she finds employment. Atsugi has most everything you can find in either Tokyo or Yokohama but on a smaller and cheaper scale especially for housing.
If it were me, I'd opt for living near my work in Atsugi. Good luck!