Tap into your inner culture lover at Museum of Haiku Literature. See if any guided tours are available or ask a museum employee for tips on some collection highlights.
You'll have no end of sightseeing choices in Shinjuku. Museum of Haiku Literature is an ideal place to begin here, but there are lots of other interesting places to consider. Tokyo Tower, Tokyo Imperial Palace, and Sensō-ji Temple are near the museum and and will cap off your day nicely.