Having been asked this a couple of times, we decided to compile a list of some (English language) Japanese home cooking recipe books. However that said, ironically our recommendations would be to check out a few websites before you buy your first Japanese cookbook.
The main reason is that the internet provides the necessary support when trying to cook Japanese food for the first time. Probably the most frustrating part will be figuring out what are the necessary Japanese ingredients, finding them, and familiarizing yourself. Cookbooks may have general recommendations on where to purchase ingredients, what can be left out, or what can be substituted, but not everything will be crystal clear.
Just Hungry is the most comprehensive site to familiarize yourself with Japanese cooking. Maki who runs the site, knows what it is like to not have access to Japanese ingredients 24/7 so all her advice is extremely helpful with lots of information on understanding Japanese ingredients, when using substitutions are okay and not, and there is also a huge community of fans all over the world who help each other. Plus Maki is very good about answering questions, though amazingly enough many of them have been answered on either the Just Hungry site or her bento focused site Just Bento. Though not recipes, her articles on The Japan Times are also very informative if you are looking to want to learn more about Japanese cuisine.
Some other recipe sites are Just One Cookbook, No Recipes, and the English Cookpad recipe sharing website. Probably the most obvious drawback about the Cookpad website is that these are translated recipes so it might be difficult to follow since many of the recipes assume you are in Japan and already are familiar with the ingredients. But once you familiarize yourself with the basics it will be a good source of inspiration.
If you are really serious, Elizabeth Andoh's books are a great read. They are not for the casual cook looking for a quick recipe, but instead are best for those wanting to really understand in depth about traditional Japanese home cooking and ingredients because everything she writes is thorough with a non-Japanese audience in mind.
Japanese Farm Food is good for someone who doesn't mind a bit more narrative in their cookbooks than just straight forward recipes and descriptions about ingredients. You will get to learn a bit about what it is like to live in rural Japan. It is of course good as a cookbook but the book is so beautiful that it will probably end up better as a coffee table book.
Kurihara Harumi's books are also an option but they are more contemporary Japanese home cooking, meaning some of the ingredients she uses include western ingredients. Just imagine a Japanese Rachael Ray so her recipes represent the modern Japanese kitchen. Her books are probably more recommended for those already with a basic knowledge of traditional Japanese home cooking. The same probably goes for some of the recipes on Cookpad.