Shinjuku N'EX to Keio Department Store?

Hi, I'm wondering if anyone might be able to give me some directions on getting from the N'EX Platform at Shinjuku Station (5 and 6) to the Keio Department Store. I have to spend a couple hours waiting at the station for someone before we actually take the Keio line. I want to avoid going up/down too many elevators or escalators if I don't need to. Is the best way to get to the department store and Keio Mall by just going out the West exit and then going back into the store? Or can you get there while staying inside Shinjuku Station? I'm super directionally challenged so thanks in advance for your help :)

A curious question and I am interested why escalators/elevators are to be avoided (do you prefer stairs), and why specifically Keio store not one like Odakyu department store next door (also in the station).
Some people might just sit in a coffee shop or Starbucks for an hour or so.

Oh sorry, I actually meant I want to avoid stairs, haha! I don't know, I'm just hoping to find somewhere to eat and sitting at a coffee shop is fine too. I just have a really hard time finding anything I'm looking for in Shinjuku ... :') I just don't want to go in the wrong direction.

Walk to West gate(exit), and go straight soon, over the Odakyu(in water-blue) signs.
http://www.jreast.co.jp/e/stations/e866.html
https://goo.gl/maps/SxPnqAJVQWo
https://i.imgur.com/48fTCnM.jpg

https://www.keionet.com/info/shinjuku/foreign/en/

we actually take the Keio line.

Please note that there are two Keio routes between Shinjuku (KO01) and (KO04) Sasazuka.
When you head to (KO02) Hatsudai or (KO03) Hatagaya Station, you choose the route so-called Keio New Line [Keio Shinsen];
trains running by the other route do not make a stop at these two stations.
https://www.keio.co.jp/english/howto/pdf/map.pdf

Shinjuku Station of Keio has a zone with gates as to each of the two routes.
There is a pathway with staircases between the two zones; however, its accessibility is very limited.
I recommend that you check how to get to a correct gate.

The (the so-called) Keio New Line and the Toei Subway Shinjuku Line are jointed at Shinjuku.
To get to a gate for this route, you can follow signs for Keio New Line and Toei Shinjuku Line.

To get to a get for the other route, you find signs for Keio Line which do not mention the subway Shinjuku Line.

Thank you for your help everyone!