Question:

I will be away from home for some days of Chanukah. Do I need to light a menorah of my own, or will the menorahs kindled by my wife and kids back home “cover” me as well?

Response:

Let’s say you would be staying at a Jewish home. Your family back home will be lighting for you, while you would see the candles lit on your host’s menorah. Then there would be reason for you not to light. Yet, even in that situation, the accepted custom would be for you to light the menorah, as the optimal practice is for each individual to light his own menorah.

However, since you plan on staying at a hotel, where no one else will be lighting the menorah, you should certainly bring a menorah along, recite the appropriate blessings and light it.

On a practical note, I suggest that you pick up some of those neat ready-made cups with oil and wicks that you can take with you with minimal mess. I also recommend that you request a smoking room, as you will be less likely to have problems with your lights there.

I also suggest that you get candle-lighting times for your destination and brush up on how to light the menorah so that you'll be ready to roll when you arrive.

Have a wonderful trip and a joyous Chanukah!

Source:
Code of Jewish Law, Orach Chaim 676.