Source article: http://www.torahmusings.com/2014/12/guests-travelers-chanukah/
First of all, as the question assumes, there is an obligation for a traveler to light candles (Shabbos daf 21, Shulḥan Arukh 677:1). If the traveler's wife will be lighting for him in his house, the custom of the Sefardim (see Beis Yosef there) would be for the guest not to light at all. Many - but not all - Ashkenazi poskim say that the guest should still light (or join the host) where he is, so the Mishnah Berurah (677:15) writes that it's better for him to listen to someone else make the bracha, but if that's not possible, to light with a bracha.
In the case where one has a host who will be lighting, the guest should give some money to the host in order to 'acquire' some of the oil being lit by his guest (Ran Shabbos daf 10, Magen Avraham 677:1). The Mishnah Berurah (s.k. 7) writes that it is better for a guest to light his own candles, but R. Eliyahu Shlesinger (Ner Ish UVeito, p. 368) and R. Hershel Schachter has told this to me as well.
If one is sleeping at home, but eating elsewhere, he still lights at home (Taz 677:2)
However, if one is eating and sleeping somewhere other than his house, and these are in two different places, then the Shulchan Aruch writes, (677:2) based on the Tur, that one should light in his place of sleeping, but the Rama notes there that the Ashkenizic custom (based on the Rashba) is to light where one eats.