Narita to Hotel Sunroute with kids via N'EX

Hi will be in tokyo around 11am in the morning saw the schedule of limo bus earliest is 2pm is it advisable to use nex and exit in shinjuku with luggage and kids ? Without using stairs thanks

Which Sunroute is this?

Hotel sunroute plaza shinjuku

Is it Sunroute Plaza ?

Narita Express stops at platforms 5 & 6 in Shinjuku Station. There is an escalator right from the platform up to the concourse, and you can exit either Southern Terrace Gate or New South gate which are very close. No extra stairs. According to the JR Shinjuku Station map there is a taxi rank outside Southern Terrace Gate. If you are going to Sunroute Plaza it is not far but if you have kids and luggage and you don't know where you are going it might be worth while. However there is another Sunroute Higashi and this is no where near the Narita Express platforms.