Easiest(60~120min): Limousine Bus door-to-door to the hotel. Limousine bus passengers can buy the special ticket with a free 1-day metropass for 3100yen. Luggage handling included.

If you take the train, you lug your bags along, and Shinjuku is not the place to do so on your first visit. Or you send the bags by courier for ~1800/pc. Hyatt Regency provides a free shuttle bus service from Shinjuku Station. The challenge is to locate the bus stop on your first ever visit.

Cheapest (98min): Keisei Express to Nippori switching to JR Yamanote to Shinjuku = 1190yen

Direct Train(90min) : Narita Express to Shinjuku = 3500yen with a 2000 SUICA fare card which is refundable. net cost 1500

Faster(67min + transfer time): Keisei Skyliner to Nippori followed by JR = 2290yen and get a free 1-day metropass