If you're a fan of live theater performances, catch a play or other stage show at Shinjuku Suehirotei. Look online to see what's still available.
You'll soon find out why this Shinjuku arts and culture attraction is visited by many travelers. If you're searching for other things to keep you busy, Tokyo Skytree, Tokyo Tower, and Tokyo Imperial Palace are in this area too. They won't take long to reach from Shinjuku Suehirotei.