This is a good question and you are looking in the right city when it comes to diamonds. There are several places to go to find diamond buyers and sellers. Moreover, there are several important points to keep in mind before you sell or buy diamonds. Let me give you some ideas.
First, if you go on 47th street between 5th and 7th avenues and around that area, you will find store after store selling and buying diamonds. It is called the diamond district. So, this would be a good place to start. These people know their diamonds and they will want to get the best price for themselves. So, you should prepare by doing research.
Second, because there are so may stores, make you compare prices and policies. This will take time, but it will pay off.
Finally, do an interest search to find other stores that might not be in the diamond district.