Eikaiwa, to bring in income while you make plans, sort out the landscape, and learn more Japanese. If you are lucky, you might find something a bit more interesting, but if you can't, its more important to get employed, get into the workforce, get some income coming in, and be productive rather than sitting around at home.
Get your name into some headhunters, or headhunting agencies. There are a number of bilingual agencies. You won't be a super-attractive candidate for them, as most make commissions based on the salary of the people they place. Therefore, they tend to focus on executives (lets say people earning more than $100,000 per year). But if you have a marketable skill/degree, you could be interesting to them.
Have your wife help you figure out how to navigate some of the online employment search sites. Daijob is one that comes to mind (just because they advertised very heavily a few years ago). I don't know if they are the biggest or best, but your wife might know better than me. These sites are 99.5% targetted towards the native Japanese employee pool, but that remaining 0.5% of companies just might have something interesting.
Get serious about learning Japanese. Start working towards earning one of the certification levels of Japanese (JLPT 4 or 5, I think those are the lowest levels). These levels are so easy to acheive, no employer really cares about them, but they at least get you on the road to becoming a bit more bilingual.
You are just out of the starting gate, so I do encourage you to remember it is a marathon. You will not get a high-paying, satisfying, ego-fulfilling career right away. And this is a super-tough lesson for you to learn. But you need experience, you need income, you need some sort of structure so that you can get on the right path, and you need to get serious about the "long-game". You also need to demonstrate to your new family that you are willing to put in hard work so that you can build a stable home for your wife. You need to understand that you may not do something very interesting for the next 3 years, but these three years will allow you to springboard into something more interesting. You also need to understand that doing something uninteresting, boring, low-paying, and potentially humbling, can be a mental drain, which also can put stress on a young family.
You didn't say what your graduate degree was in. This could be valuable to a headhunter.
