Answer: The Gemara (Menachos 44a) writes that while one who rents in Eretz Yisrael must affix a mezuza immediately upon moving in, one who rents a home in chutz la’aretz isn’t obligated to affix a mezuza for the first thirty days. Thus, one renting a holiday home in chutz la’aretz for a week or two has no obligation to affix a mezuza.
Following this, there is a machlokes as to whether one renting a home for over a month in chutz la’aretz should wait until the thirtieth day to affix their mezuzos or should do so immediately.
R’ Moshe Feinstein (Igros Moshe YD 1:179) quotes the Pischei Teshuvah (YD 286:17) who writes that one may say the beracha earlier while the Nachlas Zvi (YD 286:22) wonders whether it is ideal to wait until the thirtieth day. Thus, R’ Moshe writes that one should fix a mezuza straight away but not recite the beracha until the thirtieth day.
R’ Yitzchak Yaakov Weiss (Minchas Yitzchak 2:82) quotes the Derech Hachaim and Harei Besamim (2:219) who write that in this case the obligation begins immediately and one may affix a mezuza with a beracha when one moves in.
Likewise, the Aruch Hashulchan (YD 286:49) writes that while one isn’t obligated to affix a mezuza if one is staying there for less than thirty days, if one is renting a place for longer, their obligation to affix a mezuza begins immediately. R’ Moshe Sternbuch (Teshuvos Vehanhagos 1:644) adds that contracts nowadays are legally binding making the lease more permanent than in the past. Thus, one must affix their mezuzos immediately.
In conclusion, one who signs a tenancy agreement for more than a month should ideally affix their mezuzos when they move in.