Omakase in Tokyo

Hello friends!
We are going to be in Japan in May and we would like to try Omakase in Tokyo.
Do you have any recommendations?

Thank you for sharing your experience and greetings from Austria :-)

Omakase in what? Sushi?
Omakase means to let the chef decide the meal course, so it is available in all kinds of eateries - and not all are necessarily displayed on the menu.

For sushi, I tried this place in Shibuya: https://goo.gl/maps/4BuQQPcza2HJYVRu7
Reservation is practically a must, and can be made on line.
They had 2 omakase courses - ￥13000 or ￥8800 (they used to have a ￥4800 course, too; price is fluctuating, I guess). You can order more if you are still hungry after the course completion.
I was very impressed.

https://youtu.be/lmzs4kNZKww

Maybe you are thinking of kaiseki? The chef decides there as well, I suppose. I've never had it in Tokyo as I only usually have it at ryokans, and I've never stayed at one in Tokyo. But if that is what you are thinking of, I'd look at staying a night in a ryokan at Tokyo or close by, eg Kamakura/Enoshima or Hakone, or Nikko maybe, and have the full board.

Maybe the OP is not even looking for food but just needs to leave something up to someone. As for food terminology, however, here are some more details. In the 80s, my father would take me to bars where we'd spend long hours with the madam as she prepared dishes of all kinds one by one.

https://en.wikipedia.org/wiki/Omakase

This question made me confused, because, as Wikipedia explains already, "omakase" just means one of the style of HOW TO order, especially at fancy restaurants (like ryoteis) and does not indicate a specific dish.

If the OP still reads this topic and is a super-rich traveler enough to go to a ryotei, I would recommend you to tell the restaurant in advance that you're willing to order "omakase" style when you make a reservation. And never forget to tell them about your allergy or ingridients which you can't eat (if you have any). "Omakase" doesn't consider such kind of food trouble unless you declare.
And please keep in mind that such kind of "omakase" ordering only works in high-expense restaurants generally, not in budget-friendly restaurants, like as chain ones or izakayas. Some may offer you dishes like "Today's Recommendation" at reasonable restaurants, though, but I'm not sure that would be what you expect as "omakase".

Actually, "omakase" is not limited to high-end places at all. You can go to any cheap little restaurant and ask for "omakase" which simply means "leave it up to the chef for a course menu". As a Japanese local, I do it all the time.

Whether the place offers omakase or not is totally up to the chef and not the quality or price of the restaurant.

Meanwhile, if you look at the menu at a restaurant, you'd often find dishes named like "chef no omakase salad" or "chef no omakase so-and-so" which means "salad (or so-and-so) which is up to the chef to decide the contents of" which is pretty much the same as "salad (or so-and-so) of the day".

The Japanese word "omakase" means "leave it to the other party". If you enter a restaurant and say "omakase de onegai dekimasuka?" you're asking "May I leave it up to you to provide me a course menu of your choice?" And if you are in a business meeting and say "omakase de onegai dekimasuka?" you are abandoning your responsibility to decide what you're negotiating about.