I know of two good ways to experience Japan. I have done them both, and they are both worth doing.
The best way to experience Japan is to go on an exchange program to one of their universities. You don’t have to know Japanese before you go because they make special classes for the exchange students to learn Japanese. They also take the exchange students on a lot of site seeing trips. If you are an exchange student, the school is responsible for you, so you will have someone there to take care of you and explain things to you. You will learn a lot, and it will be the experience of a life time that you will never forget!
If you are too old to be an exchange student, teach in a language school in Japan. They are always needing native English speakers who can teach English in their language schools. You don’t have to speak Japanese before you go to do that either, but if you want to learn Japanese, they don’t automatically give you Japanese classes like a university would. You would have to ask someone at the language school to help you get a class. The people at the language school will be kind if you need help finding your way around, etc., but it wouldn’t be part of their job to take care of you like it is if you go to study at a university.