The gemara[1] says that a guest is obligated to light Chanuka candles at his host’s home, but it is sufficient to give money for some of the oil that is used to be included in their lighting. (Some say that more oil must be added in order for the contribution to be significant.[2]) The gemara adds that Rav Zeira, who used to pay toward the oil, stopped doing so once he got married (but was sometimes away from home by himself) because his wife would light for him in his home.[3]
Thus, it would seem that as long as there are bar/bat mitzva age children at home lighting, you are exempt from lighting away from home. The Taz[4] posits that a wife is automatically assumed to light with her husband in mind. However, others in the household (e.g., bar mitzva age children) should have their relative(s) specifically in mind. Yet, there are additional factors that complicate matters, and these factors are different for Ashkenazim and Sephardim.
The Maharil, one of the pillars of Ashkenazic p’sak and, especially, minhag, says that nowadays a person who is staying at an inn should light his own candles (even if his wife is lighting at home). This is because two realities have changed. One is that the place of lighting with the related pirsumei nisa (publicizing the miracle) has been moved indoors. Secondly, now it is customary that all the members of the household light. Therefore, if one of the guests does not light, others may think that he has chosen not to take part in the mitzva; they may not realize that he has a household that is lighting for him. The Terumat HaDeshen[5] rules that, even though one is exempted by his family, since there is a concept of mehadrin,[6] a guest who is interested in lighting may do so with a beracha. Moreover, in general, there is a preference that a person light his own candles rather than add on to the host’s oil.[7] This is all the more so in a case like yours where you are part of a group where everybody is a guest at a commercial institution. This is different from joining an existing household, which more naturally incorporates others.[8]
As far as where to light, the Rama[9] says that the location where people eat is the proper place to light. One could argue whether it is preferable to also light in or outside the room where one sleeps [beyond our scope], but given that most guesthouses are understandably reluctant to permit fire hazards, the lighting in the joint dining hall should suffice.
For Sephardim, there are two major differences. Firstly, the Shulchan Aruch[10] does not accept the Terumat HaDeshen’s permission to make a beracha when his household will exempt him. Secondly, the Shulchan Aruch states that when the guests have sleeping quarters with a different entrance than that of the ba’al habayit (homeowner), they should light there; otherwise, it might be suspected that the occupier of the dwelling is not lighting. It is unclear whether that situation requires lighting with or without a beracha (when there is a candle lighting at home) The Kaf HaChayim,[11] therefore, suggests hearing the beracha recited by someone who is certainly obligated. Where there is a problem getting permission to light in the room, it may be reasonable for Sephardim to light without their own beracha in the joint dining area and to try to ensure that someone lights in front of the building or wing where they sleep on behalf of all of them. Another rationale of leniency is that in a campus that is occupied by one group whose members light uniformly, the issue of suspecting one another is weaker than usual.