These are just my thoughts:
main() is a static method unrelated to object instances. We know that it exists as an entry point, that makes our program/class executable.
The thing is that in Java, everything (but primitives) is an object, so main() must be declared in some class somewhere. The code such a static method may execute is more concerned with setting up the program for execution, and delegating to our business logic (objects that actually do something) to run the application. As such, its concern is distinct from the rest of our class (which defines some data and behaviour that we are trying to encapsulate).
main() doesn't really belong with the data and behaviour of our everyday classes, as I doubt that every class needs to be executable on its own. main()'s concern is with running our program. As such, it should be declared away from our business objects, in a module of the project concerned with application launch/execution. So, as you might be guessing, I am proposing exactly what you've said not to suggest - keep main away from your classes and logic as much as possible, and only declare it in the context of an entry point to your application.
As to the location within a file itself, I don't really think it matters - as long as it is obvious that the code in that file is concerned with setting up and running the program.