If I eat by someone else but sleep at my house, where do I light neiros shabbos?
Technically you can light in either place, however the preferred place to light is the place that you are sleeping. The reason is because the place that you are eating already has someone lighting there. It is important however to be careful about a few things when lighting at home. First of all the candles should be lit in a place that is very safe, especially since no one will be supervising the candles, i.e. on a table near drapes that can get blown by the wind and touch the candles etc.
The second things is that In order to fulfill the מצוה of הדלקת נרות, there must be some benefit derived from the light of the candles. This can be done in one of two ways; By enjoying the elegance that the candles add to the Shabbos meal (כבוד שבת). Or by receiving pleasure from the light that the candles give (עונג שבת). since you are not eating near the candles you must benefit from the light of the candles, otherwise you will not be yotza hadlokas neiros. There are a number of options for you. Either you should make sure to light long candles and eat something near them when you get back from the meal. You an also read something close up to the candles, in a way that you will be benefited from the light of the candles. Alternitively you can turn on the electric lights in one of the rooms immediately before lighting your candle, and without talking out light your candles and have in mind that the electric lights are to be a part of your “shabbos candles”. This way when you get back from your meal, even if the candles have gone out, you will still derive benifit from the electric light that will still (hopefully) be burning.
Aruch Hashulchan O:CH 263-4, M:B 263-39,40, Shmiras Shabbos Khil choso 43-34, and 45-8, Shvus Yitzchok 8-2 (5), and chap. 4-2 in the name of R’ S. Z. Auerbach and R’ Eliyashiv zt”l, Sefer Kavod Shabbos chap. 4 ftnt. 4, and chap. 2- ftnt..22, that this is what they did in the homes of R’ M. Feinstein and R’ Y. Kaminetsky zt”l, Teshuvos V’hanhogos 2-157, Be’er Moshe 5-113, Rivivos Eprayim 3-162, Mishne Halachos 5-40.