I drink my coffee everywhere, but the combined Starbucks & Tsutaya bookstore between Roppongi station and Azabu-Juban station is large, exclusive and just good. And it‘s always well visited.
On weekdays by students from Tokyo universities, at weekends crowded by a mix of people who just want to be outside but don‘t like the party area of Roppongi, Students, party people who join for a coffee to get sober again etc.
Opening hours are until 4 am every day. Three large tables are equipped with power plugs (sometimes difficult to get a seat there). If you are in Tokyo and have to work, keep this place in mind.