The Shulhan Aruch (O.H. 94:1) rules that when one prays the Amida, one should face the direction of Jerusalem. Most diaspora communities tended to be west of Israel and therefore the direction of prayer would be toward the east. Rabbi Mordechai Birkat Erev (pg. 107) cites a disagreement between Rabbi Ya’akov Emden (Mor Uktzia, § 94) and Rabbi Mordechai Jaffe (Levush, § 94) regarding synagogues which are not located to the west of Israel but rather to the north, or the like. The former says expresses wonder at how the Hechal of many synagogues in countries to the north of Israel are still placed on the eastern side of the synagogue. The Levush, on the other hand, says that since there is a concept that Hashem’s Presence is found in the east, the common practice is to place the Hechal and to pray towards the east, regardless of where in the world one is.
In many instances a synagogue cannot be designed such that the Hechal is exactly in the east, either for architectural reasons or due to the orientation of the plot of land. Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II, ch. 45, § 25) writes that if one is in a synagogue in which the Hechal is not exactly to the east, one may pray in the direction of the Hechal, as long as it is roughly to the east and one would not have to turn one’s back to the Hechal in order to pray in a mostly-eastern direction. Similarly, the Hatam Sofer (O.H., § 19) says that when designing a synagogue, the Hechal may be placed such that it is not exactly to the east in order to gain more space for the sanctuary, but that it should still be roughly to the east. Rabbi Haim Ozer Grodzinski (Shu”t Ahiezer, vol. III, § 79), however, says that one may not build a synagogue in any other direction except towards the east. It seems that there is more leniency, even among those with the approach of the Ahiezer, to place the Hechal towards the southeast, if needed, since practically speaking, that is the direction of Israel for communities in North America and Europe.
If one is on a plane, Rabbi Ben Zion Abba Shaul (ibid.) says that one should estimate where east is, based on the direction of the flight. For example, if one is flying from Tel Aviv to New York, one should pray roughly towards the back of the plane. If one is flying from Miami to New York, one would pray towards to the right side of the plane. [The propriety of standing in order to pray while on a flight will be discussed elsewhere].
Summary: The Hechal should be positioned at the very least in a roughly eastern position in the sanctuary. On a plane one should estimate where the east is based on the direction of the flight.