If you are staying around the Shiodome area, it is a very easy walk to the Tsukiji outer market. I finished my Japan trip last week with a couple of days at the Conrad and had no problem with the walk

My favorite coffee in Tokyo is right around there, Turret Coffee, and it opens at 7

The outer market stalls will be starting to get going around that time as well and you would hopefully avoid the major crowds that develop later in the morning