I'm on the hunt too and have found some that are out of my price range...so if you let me know what pricing you are looking for I might be able to point you to some cars I have seen that I'm not buying--welcome to the board.
That is a good budget and should get you a clean car, most likely a GTV2000 based on what I have seen in the market [assuming you are in the US]. There is a red 1972 GTV 2000 that is very clean that I recently looked at and if I don't buy it I will send you the information to contact the seller. Also just saw an amazing 1971 1750 that is $50K if you can stretch your budget.
As many will tell you, see if you can narrow down what you want as there were many variations from the early 60s to mid 70s and then figure out what condition you want and go from there.