Well Danny, in many ways it depends how lucky you are as many of the great deals last less than a few hours here on the forums ^_^
Also when you say new, do you mean the latest series serial number models fresh from the factory and brand new in the box (BNIB) or is a 5 year old watch still in plastics, unworn with no previous owners ok too?
In any event, I've seen several new Airkings or Datejusts in your price range.
But like everyone else is saying, buy preowned and save money. Use some of the savings to get the watch serviced if its out of factory warranty. Each time it gets a service Rolex gives you a fresh 2 year warranty :)
+1 for a gently preowned GMT-IIc. Some great updates in that watch and I've seen them listed as cheaply as 6.3K
https://www.rolexforums.com/showthread.php?t=209432
https://www.rolexforums.com/showthread.php?t=208958
Good luck on your mission!