Lighting Shabbat candles is a rabbinical decree. The candles should be lit mainly to have light in the room where the family will have dinner. The Shulḥan Arukh, however, says (OH, 263:6) that a single young student who lives outside home should light a candle in his bedroom [the same applies for a girl] saying the blessing for it. In other words, if dinner takes place in a different place, then both places should have their candles lit.
The same principle applies in a case of an Hotel, when we eat in the Hotel's dinning room and we sleep in our own room, we need to have a candle in both. Rabbi Obadia Yosef (yalqut yosef, Shabbat 1, p.148) clarifies that if the Hotel does not allow to have a candle lit in the room, for safety reasons, one should leave an electrical light lit, and before turning it on, the correspondent blessing should be said.
Now, as to the Hotel's dinning room, while there is an obligation to have candles lit there, there is no "personal" obligation to light a candle in the dinning room. In other words, if someone else already lit a candle in the dinning room, there is not need for me or my wife to light another candle.
However, if someone still wants to light an additional candle in the dining room, then, there is a difference of opinion between the Sephardic and Ashkenazi tradition. Sephardim do not say a berakha for lighting an additional candle (OH 263:8) because it is considered an unnecessary berakha [berakha lebatala]. While the Ashkenazi tradition (Rama, idem) holds that one should recite the berakha on an additional candle [tosefet ora], because it adds to the splendor and enjoyment of Shabbat.
Shabbat Shalom (and Ḥodesh Tob!)
Candle lighting in NYC: 4:31 p.m.
Shabbat ends in NYC: 5:29 p.m. *
* I'm calculating the end of Shabbat at 40 minutes after sunset. In many communities they determine the end of Shabbat 50 minutes or more after sunset.
For a more detailed explanation of the above mentioned Halakha, including both traditions, see this Teshuba (Hebrew) written by Rabbi Re'em haCohen, rosh Yeshibat Hesder in Otniel, Israel