The ignorant cannot locate Avidya since he is it. He is ignorant. The Jnani cannot locate Avidya, since he sees no ignorance. He sees himself clear as daylight as Brahman. There is hence for him no Avidya, forget the locus. But why do we still ask the question then?
So the attempt has been to say that either Avidya is located in Brahman or in Jiva. This has led to the schools of Bhamati and Vivarna. Bhamati holds that Jiva is the Ashraya of Avidya. Vivarna holds that there is anyway only one Brahman, who is simultaneously the locus and object of Avidya.
The next question is, is Avidya real like my desires or is it unreal, in the sense that it has no basis for its existence?
One contention is that Avidya is just a superimposition, an Adhyaropa that has been made in the Upanishad, so that one can do the negation, Apavada and arrive at Brahman. It has no reality and is just a word used to get us back home.
The rather mainstream contention is that Avidya is Bhavarupa, or yat-kincit-bhavarupa, in the sense that it holds a certain amount of reality, just like your desires etc. This is naturally also mithya, in the sense that Avidya appears because Brahman is there. It cannot appear out of thin air.
Are Maya and Avidya the same?
Some say they can be used interchangeably. Maya seems to be attributed to Ishwara, who is wielding it. Avidya however has a more negative connotation, that I am subject to it as a Jiva. Here again the views diverge between different vedantins.
If we take Avidya and Maya as synonyms, then the sequence that follows is – Ishwara was subject to Avidya, then he realized that he is Brahman, then he because of his Upadhi as Jagat, became the wielder of this Avidya.