Not unless you take a romantic side trip to Louisiana or New Hampshire!
New Hampshire has no sales tax statewide, for anyone. Louisiana has a tax-free scheme for foreign visitors; show a non-US passport in your own name, and the tax is left off (you do have to fill out a form, and not all shops participate, but most fine jewelers do.) There are no branches of Tiffany & Co. in either state, however. New Orleans has a plethora of fine jewelry dealers; you can certainly buy antique Tiffany there if you have a mind to.
BTW, as of last year, it is also possible to elope to New Orleans. There is no longer any waiting period for non-residents; you can get a license and get married within the hour, 7 days a week.