There are four opinions where on Har Habayis the Beis Hamikdash was, they are:
1)dome of the rock is where the Kodesh Hakodoshim was.
2)dome of the rock is the place of the mizbeach.
3)Beis Hamikdash was in the south part of Har Habayis, in the empty space between the mosques.
4)Beis Hamikdash was in northern part of Har Habayis.
Each opinion can be sub-divided into a few opinions, arguing exactly the five-hundred amah square was, and the size of an amah.
(For a good summary of most of the opinions, as well as the problems with each one, see אוצר ירושלים והמקדש by Encyclopedia Talmudis, pages 325-345, and the diagrams in the back.)
One of the big questions about the Beis Hamikdash is where the Beis Hamikdash was on Har Habayis. The Mishna (Middos 2:1) says Har Habayis was five hundred amos by five hundred amos, and the Azarah was farther away from the south wall than from the east, farther from the east than from the north, and the least space was in the west. The meforshim give different numbers to explain this, but they are all random numbers, not saying that this is how it was. (The Tosfos Yom Tov says 250 in south, 213 in east, 115 in north, and 100 in west. The Tiferes Yisroel quotes the Shiltey Hagiborim who says 265 in south, 250 in east, 100 in north, and 63 in west.) It would seem that we could get a pretty good picture of where the Azarah was, but there is a big problem, Har Habayis, how we see it now, is bigger than five hundred amos. As it is now, the south wall is 584 amos, the east wall is 968, the north wall is 659, and the west wall is 1013 amos. (I am using Rav Avraham Chayim Na'eh's amah, which is 18.95 inches or 48 centimeters.) The answer to this question is that Yosifun writes (War of the Jews 5:5:1) that king Hurdus (Herod) expanded Har Habayis. But the question is, where in this big area was the original five hundred amos, which only that part was sanctified with the Kedusha of Har Habayis, and where in there was the Azarah?
I have added a new video of the Lishkos on the northern side of the first Beis Hamikdash..
My name is Mendel Lewis.
Hashem said to Yechezkel, "Its reading in the Torah is as great as its building. Go and say it to them, and they will occupy themselves to read the form of it in the Torah. And in reward for its reading, that they occupy themselves to read about it, I count it for them as if they were occupied with the building of it. (Tanchuma tzav 14)