Yes, you have to report the sale. (You do not report a purchase on your tax return.) It makes no difference what you did with the money from the sale.
What you might be thinking of is an old rule that you could defer (not eliminate) the gain from selling your home if you used the money to buy a new home. But that rule was eliminated in 1997, and even before 1997 it applied only to your primary home, not to a second home or a timeshare.