Need wristwatch help!

A Jaeger Le Coultre Reverso in s/s under $2000 can really only be found as a quartz movement. However Cartier can be a good choice as in their iconic Santos, and perhaps Tank Francaise, and Tank Americaine. All three of these watches are available as a mechanical movement. The price range new for these are a bit over $2000 but used or otherwise should be just at that point. Another option is a Bedat & Co watch. Their creations are also in a Tank style with mech. movements. Pricewise Bedats are not as high priced as Cartiers. Baume & Mercier is again a good choice in terms of your criteria.

I am not a big fan of rectangular watches in general, but I really like the Girard-Perregaux Vintage 1945 series.  Girard-Perregaux (GP for short) is a great, and vastly underrated, company that uses all in-house movements.  This model is right under your price point.  (I assumed that you wanted a steel case and not necessarily a bracelet.)  I have never purchased a watch from this particular internet vendor, but they offer a 3-day return policy and I have heard that they are quite reputable.  The watch in question is a bit dressy, so it may or may not be what you're looking for.