Sumo would have been out of question anyhow due to it being sold out, you would pay a hSefty price for a ticket if you could get one i.e. $250.
Oddly when I there in March I killed both those birds with one TV
Had sumo matches for awhile then a baseball game, japanese baseball commentary is flipping hilarious, lots of "Hmmmmm"s
Shinjuku nightlife is there and there are an insane amount of clubs and bars but they might not be a big size as your used to.
The "famous" Studio Alta meeting spot by Shinjuku station, it's once huge screen looks quite dated now