Ticket to Shinjuku:
NEX: 3500 rt if you use the SUICA+NEX package(and return the SUICA card for close to full refund). 1:30 hrs one way
Keisei Skyliner: 4800 rt to Nippori + 360 rt to Shinjuku : 36 min. + ~ 10 minute transfer time + 20min = 66min one way . Alternatively Ikebukuro is 10 minutes closer and is just as good as Shinjuku for a short visit.
Of course there is the added problem of getting lost inside Shinjuku station. If you are a 1st time visitor, probably Ueno or Ikebukuro is a better destination for a few hours.