I faced your situation before. There are extremely dense rubber mats (about an inch thick) called "stall mats", each about 3' x 4' that are used in horse trailers -- cost a total of $34 at Tractor Supply (yes, I get that's not going to be in Manhattan, which is yet another reason I don't live in a big city. Awesome store.) that work extremely well for soundproofing. They cut easily. Very dense, same rubber as a car tire.
I've seen them in use in CrossFit places in Manhattan, so I presume someone ships them, even to Manhattan. Extremely heavy, so be warned.
You lay one layer on the floor, then a layer of plywood, and then another layer of the mats on top. This is extremely effective at stopping sound transfer.
Put an area rug on top so you don't look like a CrossFit gym
You could do a big room for $200.
As a bonus, you also now have a place to do dead lifts and drop your weights.
Your house will also smell like a tire store for a week.