
Surviving as a vegetarian in Japan is full of challenges. There are even fewer options and that too pricy ones for vegans(ビガン) in Japan with most products having some element of non-veg food.
But, if you are ok to give up vegan-ism for a day or two and turn to eating milk products or may be go up to eating eggs as well then I can tell you many options.
As is the case with many people who switched from eating non-veg foods like meat/fish and all, to being a vegan they are still ok to some extent to eating milk and egg products, I will continue.
Mexican Restaurants for vegetarian in Japan

So, there is this Mexican restaurant called Guzman-Gomez in the ever happy street of Harajuku and Ikspiari near Disney land, here you can order your very own vegetarian Quesadillas, Fajitas or even Tacos by opting for the vegetarian (ベジタリアン) option. They have cheese and some sauces inside which sure have eggs and milk inside them, but sure its a great option for vegetarians. The dishes are only about a 1000 Yens (10$) and you can get your stomach full by having just 1 Quesadillas or a Burrito.
Indian restaurants for vegetarian in Japan

As you must already be knowing that there are many many Indian restaurants and most have atleast 1-2 curries which are vegetarian friendly. But Naan is made up of egg and milk and curries also use some cream so for my Vegan friends, you can just request the waiter to not add cream to your curries and replace Naan with rice, that would be a great spicy Vegan dish for you!
Italian restaurants for vegetarian in Japan

There may be minimum of 2 Italian restaurants in any neighborhood of Tokyo and at least 1 in 2 blocks else where in Japan. And these Italian restaurants are a blessing in disguise for vegetarians in Japan as they offer 1 pizza and 1 pasta as default for vegetarians. All menus in Japan have Margherita pizzas containing only tomatoes, cheese and basil and no meat/non-veg component. And 1 pasta which is made of tomato sauce with the option to remove the beacon by asking the waiter to 肉なし (nikunashi – remove the meat). And 100% places will be happy to help and remove the meat for you. Also, some restaurants even have cheese fondue which is definitely an option for vegetarians in Japan.
There are so many high end and reasonably priced Italian restaurants that if you are a vegetarian, you can take your Japanese date to one of these fancy restaurants. One of the chains one doing this quite well is Vansan Italian restaurant. They also serve very fine wine with delicious pasta and tempting cheese fondue.
Other local options for vegetarian in Japan

Another one that I discovered recently is MOS burger. They are not Vegan friendly (or may be they are since I did not ask them about all the ingredients), but one thing is for sure that they are vegetarian friendly.
There are some burgers that allow you to replace the patty with Soy patty and it makes it a vegetarian dish. It is mentioned in small brown letters under the picture of the dish in the menu.
They have some vegan options in the form of Kinpira burger which is a rice burger. Also, I will update here when I get to know that the Soy patty burgers are vegan or not but for now I am sure they are at least a good vegetarian option.
Recent update as of 2024 is that even Freshness Burger has 3 soy meat options for vegetarians in Japan. Their Soy Avocado burger is to die for and personally it is the best vegetarian burger I have had in Japan for this price. Please note that this burger has eggs and milk used as ingredients for cooking, so it is not purely vegetarian and not vegan as well.

Image Source and for more information: https://www.freshnessburger.co.jp/menu/hamburger/soy_avocado_burger
Then there is Coco Ichibanya (Curry House) which is a savior for vegans in Japan who want to taste the Japanese curry. Here, you can find a Vegan menu (provided you are in a foreigners friendly area of Shinjuku, Shibuya, Aoyama Itchome or the like). Just go to any of these chain restaurants of Coco Ichibanya and ask for a vegan menu, they will even speak English if they have a vegan menu or if not they will simply say no or don’t understand your question at all (because yeah they don’t even speak English).
Do try this vegetarian curry which may also be vegan as it only uses plant based ingredients though not explicitly mentioned as vegan. Also, this vegan ramen from Tantan is a delight if you are craving for instant ramen.

Other Japanese dishes include some specific types of Seaweed onigiris, for more info please check here. Also, it is possible to eat Japanese pancakes okonomiyaki in a vegetarian way, this can be done in restaurants where we need to cook ourselves and we can choose to not put the pork in the okonomiyaki.
Check out here for more info to help residents in Japan.
Thanks! I also use HappyCow App to survive as Vegetarian in Japan.