May one to walk in areas in which there are women who are not modestly dressed?
Due to the grave prohibition against staring at the beauty of a woman, the question is raised regarding walking in public, in immodest areas, and if or how, it is to be avoided.
If another path is available: It is forbidden for one to walk in areas in which women are not modestly dressed if another path is available that does not contain immodest women. One who nonetheless goes through the immodest path is considered a Rasha. This applies even if one is sure of himself that he will not give into the temptation to look at the women. [The definition of another path available is that there is another viable option to reach one’s destination that will not take extra time or cost more money. If, however, it will take extra time or cost more money, then one is not obligated to go the more modest route, although certainly he is considered a Chassid if he does so. The same would apply if one is traveling to a certain store, that contains immodestly dressed women, that if another modest store is equally available for the same time and price, then he may not go to the immodest destination.]
If another path is not available: It is permitted for one to walk in areas in which women are not modestly dressed if he is going there for a purpose and there is no other way to get to one’s destination. Nonetheless, one who closes, or turns away, his eyes while walking, and avoids seeing a woman as much as he can, is considered a Chassid, and on him it says “Otzeim Eiynav Miros Bera.” There is, however, no obligation to do so. [Nonetheless, it always remains forbidden to stare, or take a second glance, and only the basic sight necessary while walking is permitted. Likewise, one is to walk in a way that prevents him from seeing the women as much as possible, as explained next.]
How to walk in public: Every man is obligated as much as possible to walk with his head facing in a downward direction, when walking in public, in the streets, in order so he does not see women, and walks in a humble manner. Nonetheless, one should not bend his back, or have his head bent too much to the point that he cannot see the people in front of him. Rather he is to walk in an average bent manner so he could see the people walking towards him (without having to lift his eyes too much).]
 Bava Basra 57b; See also Bava Kama 48a; Piskeiy Teshuvos 75:6; Sefer Histaklus Behalacha 4 footnote 8
 Michaber E.H. 21:1; Tur 21:1; Riy, brought in Beis Shmuel 21:2; Orchos Chaim 2:13; Rabbeinu Yona Igesres Hateshuvah 19:20, brought in Beis Yosef 21; Braisa in Avos Derebbe Nasan; See Eiruvin 18b “One who gives money to a woman in order to look at her, is not saved from judgment of Gihennom”; Nedarim 20a “One who stares at women in the end will come to sin.”; Avoda Zara 20a “One may not stare at a beautiful woman even if she is single, and may not stare at a married woman even if ugly”; M”B 75:7
The reason the Torah prohibited looking at the beauty of an Erva: 1) Leads to sin with the Erva. 2) Leads to Zera Levatala. 3) Is intrinsically a sin to receive sexual pleasure.
 Bava Basra ibid
 Rashbam ibid
 Piskeiy Teshuvos 75:6 footnote 65
 Gemara ibid as explained in Rashbam; See also Brachos 62b that when walking outside, one is to avoid looking in areas where women are found.
 Gemara ibid; See regarding the allowance to see a woman in a mere glance [even immodest] so long as one does not stare, or look for pleasure: Admur 75:1 “Some Poskim permit Davening opposite the uncovered area of a woman if he does not stare at her, even though he sees it at a glance, as the entire prohibition is due to it causing forbidden thoughts, and only staring can cause forbidden thoughts.”; So rule: Rabbeinu Yona Brachos 25; Rambam Shema 3:16; Beis Yosef 75 in name of Rabbeinu Yona; Makor Chesed on Sefer Chassidim 9:2 that “Histaklus” means to stare; Sefer Chassidim 1000 that may look at woman while talking to her; Rosh brought in Sefer Chassidim Tinyana 99 that whenever it says Histaklus means stare, and hence an innocent glance at a woman is permitted; [See however Smeh C.M. 154:14 who says Histaklus means a mere look and not stare, while Reiyah means to stare.]; Rashal Kesubos 2:11; Yosef Ometz 474; P”M 75 M”Z 1 “If he sees and gets pleasure he transgresses and if not it is permitted”; M”B 75:7 “A mere unintentional glance alone without pleasure is permitted”; Emek Sheila 52:1; Salmas Chaim 438 ; Piskeiy Teshuvos 75:6-7; Poskim in Nitei Gavriel Yichud 55:3 footnote 6; Story in Avoda Zara 20a that Tanaim said “Mah Rabu Maasecha Hashem when saw a beautiful woman”
The reason: As he is Annus, and in a case of Onnes the Torah exempts from liability. [ibid]
 Bach 1 “When he sees the woman he is to close his eyes”; Poskim in previous footnote
 Igros Moshe O.C. 1:40 regarding Shemiras Eiynayim; Piskeiy Teshuvos ibid; See Admur Basra 2:5; Kama 2:7; Michaber 2:6 regarding the general requirement to walk in a humble manner, in a way that he sees the ground near his feet.
 These parentheses are in the original