In Mandarin translation of Little Red Riding Hood that can be found around (Grimm Stories, BaiDuBaiKe), mother warns Little Red Riding Hood: "外婆家的时候，别忘了说‘早上好’，也不要一进屋就东瞧西瞅。" How would you translate 东瞧西瞅 in this sentence? I have seen translations like "look around" but it does not seem to make much sense in the context.
this structure 东V西V could means:
1 do sth repeatedly and blindly
2 do sth repeatedly and leisurely
3 do sth repeatedly and curiously
4 do sth repeatedly
In your sentence, it means "keeps looking around curiously".
东跑西颠, 东倚西靠 keeps XX leisurely
东躲西藏, 东拉西扯: keeps xx blindly
东奔西跑 just means "run around here and there", doesn't imply more information.