Salary for family of 4 in Tokyo

How much should you have as gross salary (before tax) to live confortably in Tokyo when you have family of 4 members?
How much will a rental of a appartment or a house be for family of 4 (2 kids)?
How far away can you live from Tokyo centeral ?

There are a couple things you'll need to decide/think about before putting together a budget.

Tokyo is a bit city, and rents vary wildly depending on the specific neighborhood. Obviously, the further you are from the center of the city the cheaper rent gets, but the trade-off is a longer commute. So the first question is where are you going to be working, and how far are you willing to commute?

You also mention having kids. Are they going to be sharing a room, or do you want them each to have one of their own? Do you want a dedicated living room, or are you OK with just a kitchen/dining space and bedrooms?

Speaking of those kids, are they going to be going to public schools, or do you want them in private, or perhaps international, schools? That, again, will affect your budget.

Almost everyone in Tokyo commutes by train, but do you want a car for weekend family excursions? That'll require a parking space, which is an additional monthly expense.

Most apartments are small in Tokyo (unless you really have enough money, or company arrange)
I think you should first check where you want to settle and win more information by yourself.

It greatly depends on how old the kids are and what plans you/they have for their future. For example, if they intend to proceed to senior high school and then to university, even majoring things like science or medics, you need to be saving a lot, both for their education and housing. On the other hand, if you intend to work in Japan for only a few years, and are thinking about "living comfortably" only during that time, that's a totally different story. Still it depends on what kind of schooling you are considering for the meantime.

The potential biggest expense is education for your two kids. Do you want them going to an international school or a local school? How old your kids are will significantly change what is possible along with their home language. For example, international schools start at $10,000 USD a year for an Indian school to over $30,000 USD for ASIJ. If you have teenagers, I personally would not send them to a local school unless that they can speak, read AND WRITE Japanese. Note that it takes years to learn to write academic Japanese, thus the reason I laugh at people who think they can learn it in 6 months. If you have younger kids, then the right local school could be a great fit.

When choosing housing, choose something closer to the school specifically if they are younger. Housing away from train stations is cheaper but it's also less convenient. Expect 120,000 yen a month to be a monthly housing starting point but it may have gone up since I lived in Japan.

Note that setting up an apartment on Japan is expensive as you have to buy everything, pay several months deposit and key money and some people can have trouble finding a place to stay.

Expect 400,000 yen as a beginning for setting up an apartment without rent, deposit and key money. This should get you the basics but take your time and you don't need everything straight away

Before you ask for answer you should at least give some info such as

what is comfortable for you ?
Some earn 200K per month can live comfortably, while those with 500K don't.
It is very subjective depending on your lifestyle.

What kind of job/industry you will be working or been offered?
Others can then give you a estimate base on the industry/experiences.

Family.
What do you mean by kid? Age group will be much appreciated.
20 years old can still be a kid to someone eyes.
Then people can advised or point you to available education be it public or international school.
So what is your plan/view on your kid education.

And so on...

And this thing been asked/discussed till kingdom come, and most of the time people just come here and ask without giving much information, hoping that people can read their mind. Once they got their answer most just went poof without giving any respond.

To OP please use the "search box" and type in your username and see what wonder it can give you.