Let us suppose that today is Monday and that a Scrum sprint starts today. Should Sprint Planning for this sprint be done today, or should Sprint Planning have been done on Friday?
Sprint Planning for the current Sprint is contained within that Sprint. In part, this ensures that planning isn't wasted on features outside the scope of the current sprint, or on stories that may change or be re-prioritized within the Product Backlog before they are in scope.
Sprints Contain Both Planning and Execution
Canonically, Sprint Planning is contained within the Sprint. As explicitly defined in the Scrum Guide:
Sprints contain and consist of the Sprint Planning, Daily Scrums, the development work, the Sprint Review, and the Sprint Retrospective.
— Scrum Guide, Schwaber and Sutherland. 2013: p. 7.
Broadly speaking, the intention is to treat planning and execution as a vertical slice that can deliver a potentially-shippable increment. By making Sprint Planning part of the Sprint itself, Scrum ensures that planning is tightly coupled to the current state of the project, the current capacity of the team, and the immediate Sprint Goal.
In other words, Sprint Planning is a form of just-in-time planning that is focused on what can be achieved within the current sprint. Longer-range planning can be addressed in Backlog Grooming, or by other meetings or processes that suit the self-organizing needs of the Scrum Team.
Convention would be to do it as the first activity in the sprint. In reality, it doesn't matter too much when you do it provided the team is happy with the timing and it's close enough to the start of the next sprint that everyone can remember what was discussed.
The important part is that it's a consistent ceremony that happens every sprint.
I have tended to have a check point on the Monday so that everyone is sure what we're delivering but for anything but the most basic of projects the sprint planning should be done in the previous sprint before because you need time to dive into those user stories and ensure you have enough detail, know what the quality criteria are and that this is agreed with the customer.
If you wait until Monday to start your planning, then unless you're in the holy land of having an engaged customer on site you may not be ready to start until almost halfway through your sprint.