Living near one’s parents:
It is proper for one to live near his parents in order so one can properly honor them and help them with their needs. This especially applies once parents are old. Nonetheless, this is not necessarily an obligation, and it all depends on the circumstance of the child and parent and the reasons for not living in the same area as the parent [i.e. Chinuch, cheaper housing, marriage].
 See Michaber Y.D. 239:8, based on Teshuvos Harashba Meyuchasos Leramban 272, “If one swore to live by his wife’s family, then even though that by doing so he will nullify honoring his father and mother, it is not considered that he is swearing to nullify a Mitzvah of the Torah”; Binyamin Zev 281; Maharam Shick Y.D. 208; Megillah 17a that Yaakov Avinu was punished for the 22 years that he was away from home; Shemos Raba 34; Sefer Chassidim 564; Minhagei Maharil Likkutim Tzadik; Avnei Nezer O.C. 535:11 “From the above we learn that ideally one is to live next to his parents in order to serve them”; Yifei Laleiv 3 Kuntrus Achron Y.D. 240:4; Meiah Shearim 16 [p. 71]; Ish Matzliach Y.D. 1:30; Lehoros Nasan 5:53-7; Pesakim Uteshuvos 240:15 footnote 128; Encyclopedia Talmudit Erech Kibud Av Vaeim Vol. 26 p. 379; See Likkutei Sichos 39:298 to not live next to them if doing so will cause a Nissayon in Kibbud Av Vaeim