It helps to know where you live, and also what kind of Whitey you would settle for. The western whitetails in Wyoming, Idaho, etc. that you can get a tag for are generally lower trophy quality than the those hanging in midwest . That being said there are opportunities to hunt them pretty much every year in those western states if you know where to apply. Montana is also a great whitey hide-out in the west. Sometimes you need to pay a trespass fee because they mostly live on private land, but most are relatively reasonable.
Texas...all sorts of options further east.
Best of luck