What are some ideas for an interesting focused thesis on Othello employing one critical perspective (New Criticism, feminist criticism, psychoanalytical criticism, Marxist criticism, deconstructionist criticism, reader-response criticism, postcolonial criticism)?

There are many interesting critical perspectives that could be discussed. Assuming the use of "thesis" in the question means this will be for an essay or other long work, it is important to choose a perspective with a significant amount of evidence that can be discussed. Any of the choices from that list would work; however, some have more material than others.
Perspectives requiring historical analysis can require more external references but also have nearly unlimited arguments that can serve as a thesis. Given the setting of Othello, a postcolonial criticism would be very interesting. Postcolonial criticism looks at the relationship between ruling powers and colonies, generally to show exploitation of the colonies' land. Shakespeare used the long struggle for control of Cyprus between Venice and the Ottoman Empire as part of the setting of Othello. The fact that the hero is an outsider and the villain is a Venetian could be used as the basis for a postcolonial criticism.
A new historicist perspective also incorporates historical evidence. New historicism argues that the social environment of an author when a literary work is written plays a critical role in shaping the meaning of the final piece. Race is prominent in Othello, as the titular character is "Moorish," perhaps African, in a predominantly white city. While slavery in 1604 was not practiced to the extent that it later would be, some Africans had already been brought to England as slaves. These early interactions could be used to analyze Othello's role in the play.
These are just two options from the list, and each criticism has many potential focuses.