FRIDAY, BEFORE SHABBAT BEGINS: Every night we light Hanukka candles at or after sundown, but today, Friday, we should light the Hanukka candles before sunset (sunset in NYC is today at 4:28). Moreover, we should light Hanukka candles before we light Shabbat candles. Today, in NYC the time to light Shabbat candles is 4:10pm. Therefore we should light Hanukka candles a few minutes before that time.
There is another rule for Hanukka candles on Friday: while every night the candles should last at least for half an hour, if you light at nightfall, on Shabbat eve Hanukka candles should be prepared to last for more time, because we want the candles to be visible at nightfall. So, make sure your candles are long enough, or have enough oil to burn for at least one hour and a half.
In Synagogue we should light candles ideally after Minha. But if that is not possible or if it might get too close to sunset time, candles should be lit before Minha.
SATURDAY NIGHT: Once Shabbat is over (after 5:10 pm. NYT), at home you should first recite the Habdala and then you should light the Hanukka candles. In the Synagogue, for practical reasons, we first light the Hanukka candles and then we recite the Habdala.
SPENDING SHABBAT OUT: If you are spending the whole Shabbat at your parents/in laws, etc., once you are at their house, you (and spouse, children) are considered part of the extended family of your parents, and since you also partake the same food, boarding, etc. you are included in their Hanukka candle-lighting without any further requirements. So, you don't really need to light your own Hanukkia.
However, if you and your family are going to your parents/in laws/relatives house after Shabbat began, for dinner, then you should light Hanukka candles normally at your own house. In this case, it is recommended that you don't leave your house while the candles are lit, to avoid any fire hazard!
Shabbat Shalom and Hanukka Sameah!
Shabbat candle lighting in NYC 4:10 pm
Shabbat ends in NYC 5:10 pm
(Psalm 120:7) אני שלום וכי אדבר המה למלחמה
Nine resolutions against Israel pass in one day at U.N. General Assembly meeting * Interpreter, believing microphone to be off, says Israel is the only focus when bad things are happening all over the world * Awkward laughter ensues