You go away to your family / friends for Shabbos Chanuka. You are returning home Motzei Shabbos. Should you light Chanuka candles at your host or return home and light your Chanuka candles?
As always, check with your rabbi, but here's the concepts as I recall them:
It's usually best to light at home. The problem here is the concept that if it's really too late at night, you're not accomplishing pirsumei nisa -- publicizing the miracle -- if no one is around outside to see the candles.
These days, shabbos ends around 5:30PM, and people are certainly still out on the streets until -- 8PM? 9PM? What time do most stores close on a Saturday night? (And yes, there's discussions about the all-night convenience store people ...) So if you're home promptly enough, you're fine, just light at home.
If you get home late enough that no one's left outside anymore, there's still a more limited concept of pirsumei nisa as long as your spouse and/or children are around to see you light.