There are so many types of ramen so you will have to find what is your favorite kinds.
I hear a lot that tonkotsu ramen is favorite from people who come from outside of Japan. Among tonkotsu ramen places, Ichiran seems to be one of the favorites. I see many tourists lining up for Ichiran.
If you want to go more simple and healthy, try Yuzu Ramen from AFURI. They have great broth and light taste. Their cold ramen and tsukemen were also really good. They have vegan option as well.
If you want to try something unique, visit Kazami in Ginza. They have sake lees (sakekasu) ramen! I was surprised to see the menu, but actually it was quite tasty.
My favorite at the time now, is Daiki near Yushima Station. Yushima Station is near Ueno area. (I think it is a walkable distance from Ueno Park) They have simple shoyu (soy sauce) based broth, and because they are simple, I could feel the difference from other ramen shops.