You can place them on a diagonal, which will avoid any problems with support, but it may not be your cup of tea.
If the joists are properly sized, and you have at least 3/4" plywood underlayment, you probably could run parallel to the joists.
If you have strip underlayment, that precludes going parallel unless you glue and screw at minimum 1/2" plywood to the existing underlayment prior to the flooring.
I know that you you're asking a 'visual preference' question, but mechanics count heavily.
That said, if you place the flooring so that it goes side-to-side across the doorway, it will make the room look wider that way, despite its being square to begin with.
Run them the other way and the room will appear longer, front to back, as you walk in.
Hope that helped somehow.