Well,
you don't need to walk from the east side to the west side of (JR) Shinjuku Station,
because you can get to near Shinjuku Omoide Yokocho by subway instead.
Shinjuku Station of JR and Shinjuku Station of Odakyu are different stations.
Please pay attention
not only to the name of a gate or exit/entrance but also to of which station it is.
(Your phrase "east gate" is about the JR station
and "west or south gate?" is about the Odakyu station.)
Odakyu officially uses the name "West Gate Above Ground"
to refer to one of the two gates who are close to each other;
the other gate is under the ground.
will go Omoide Yokocho for tiny food shop (east gate) On a map,
Shinjuku Omoide Yokocho is
east next to Shinjuku-nishiguchi Station (E-01),
which is on the Toei Subway Oedo Line.
(Practically the alley is on the ground
and the station is mostly under the ground.)
https://www.google.co.jp/maps/place/1+Chome-2+Nishishinjuku,+Shinjuku-...which side I need to book a hotel near Shinjuku station? next morning will take Odakyu train There are some hotels around Shinjuku-nishiguchi Station,
for example,
Ibis Tokyo Shinjuku
and Nishi-Shinjuku Hotel Mystays.
It's a walking distance, I suppose,
from one of these two hotels to Shinjuku Station of Odakyu.
You see some landmarks on and around your way to the Odakyu station.
A UNIQLO shop is in Shinjuku PaLeTTe complex,
which is south next to the alley.
A BIC CAMERA shop is in Odakyu HALC,
which is the annex of Odakyu Department Store Shinjuku Main Store.
Going on the west side of the alley to the south,
you see from near the south end
the UNIQLO shop over the road,
and the BIC CAMERA shop diagonally across the crossroads.
You cross the zebra crossing to the south,
proceed for about 200 to 250 meters,
then find on your left the Odakyu station's entrance for West Gate Above Ground.
morning I will travel from Ueno to Shinjuku station In the following thread,
you say you will stay at Hotel Mystays Ueno Iriyaguchi.
https://www.japan-guide.com/forum/quereadisplay.html?0+162749This Ueno hotel is near Inaricho Station (G-17),
which is on the Tokyo Metro Ginza Line.
- Map of subway Inaricho Station (G-17)
https://www.tokyometro.jp/station/yardmap_img/_station_G17%E7%A8%B2%E8...You can take a train departing at Track 1
until (G-15) Ueno-hirokoji Station,
walk for a few minutes outside the ticket gates
to Toei Subway Ueno-okachimachi Station (E-09),
catch a train departing at Track 1
(for Iidabashi and Tochomae) on the Oedo Line,
and disembark at (E-01) Shinjuku-nishiguchi Station.
- Map of subway Ueno-okachimachi Station (E-09)
https://www.kotsu.metro.tokyo.jp/subway/stations/ueno-okachimachi/i/so...- Map of subway Shinjuku-nishiguchi Station (E-01)
https://www.kotsu.metro.tokyo.jp/subway/stations/shinjuku-nishiguchi/i...Exit D3 of Shinjuku-nishiguchi Station is close to the north end of the alley.
When you hope to avoid stairs,
you alternatively can choose
Exit D1,
which is at the entrance of Shinjuku PaLeTTe complex
and close to the south end of the alley,
or Exit D2,
which is on the other side (= west side) of the station.
