If the lighting is taking place by his doorway (either of his room/yard/house), then optimally it should be placed higher than 3 tefachim off the ground, and lower than 10 tefachim. Retrospectively, even if he varied from these measurements, the lighting is still valid. Yet, lighting the Menora higher than 20 Amos is invalid, and the Menora must be relit with a blessing.
If the lighting is by the window (as opposed to the doorway) that faces the public domain, then the Menora can be lit with a blessing with no qualms despite the window being more than 10 tefachim off the floor of the house.
Where does one who dwells in a multi family residence light the candles of Chanukkah if his apartment is over the 20 Amah limit from ground level?
The Mishna Berurah is of the opinion that he should light inside his house by the entrance to a room opposite the Mezuzah. Some present-day authorities rule that if there are other residents living at the same height, then the Menora should be lit in a window facing those residences.