Where is the best place to live in Tokyo?

It depends on how much you earn.
1) Annual income is more than $300,000.
You can live high-end condo around Azabu. Roppongi Hills Residence (right) and similars will cost you from $6K to $30K a month. That famous convict Horiemon was also living here (he is temporarily moving to a prison for what he has done.)
2) Annual income is around $100,000.
In that case, you may like to live around Meguro, Setagaya area.
Not too expensive, but still somewhat high-end locations are available.
3) If you earn less than $80,000 in a year, you might give up living in Tokyo, and find a place somewhere beyond rivers.