Hi Polskifil,
The first place to start is the tutorial post here which has all the basic information, steps, and guidelines that can help you make the best possible choice. Your budget is certainly plenty to buy a high quality mattress.
Once you get to step 3 … then post #2 here has the better options and possibilities I’m aware of in the NYC area and post #7 here also has a more categorized list with more detailed descriptions of many of them.
Of course if you have any questions or comments along the way feel free to post them here and I’ll certainly do my best to answer them 
Phoenix