Hello and welcome! There are plenty of good horns to be found in that sub $2000 range. Not a whole lot of professional models in that area, but lots of good intermediate/"basic pro" tenors to choose from. If you are set on a Yamaha, you should be able to find a good used Yamaha 52 for under $2k. You might also think about some of the vintage horns, like a good Conn or Buescher. Some of the newer Taiwenese-made saxes may also be found for under $2000. In any case, make sure the pads are in good shape before you buy, don't always just take the seller's word that "it is playing great" Good luck in your hunt.

The Phil Barone horns are head and shoulders above anything else under two grand.  He offers two basic models.   The "classic" offers a focused Selmer type sound and the "vintage" offers a deeper American vintage (Conn etc.) sound. They are reportedly a lot like the Mauriats.  

http://www.philbarone.com/store/category/saxophones/tenor