You need to change your status from F to B in order to remain past your F visa authorized time.
New York Immigration lawyer. This advice does not create an attorney client relationship. No specific legal advice may be offered by the lawyer until a conflicts check is undertaken. Information sent through a web form or via email may not be treated as confidential. Please accept my apologies for spelling mistakes.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.
If you are coming back as a visitor, it does not matter that your F-1 has expired. If you want to stay in the US to travel, you can file for a change of status. However, you would need ample evidence that your intent is indeed to visit, including funds for your travel, duration of your stay and and itinerary.
The herein content is for general informational purposes only, and may be predicated on incomplete facts. It should not be relied upon in making legal decisions or assessing your legal rights or risks. Neither does the herein reply create an attorney-client relationship.