I'm a recently retired realtor in Westchester and life long NYC area resident. I have the perfect solution for you. You need to expand your search into the suburbs. Start looking in Westchester County, Nassau County and New Jersey along the Hudson River. Housing prices is about 1/3 - 1/2 cheaper than similar homes within NYC. Commuter transportation is excellent and commuters can leave their homes and be at Grand Central or Penn Station within 30 - 45 minutes depending how far away they are from Manhattan. NJ has trains that go to Wall St. I think. You will get much more square footage or living space in the suburbs than you will in the city.
Examples: 2 bedroom + 2 bath co-op - $200 - 400,000. depends on neighborhood / town and condition of the co-op unit.
2 bedroom + 2 bath condo - $300K - 1 million depends on town and condition of condo.
A 2 bedroom co-op or condo ranges from 800 - 1500 square feet.
A 3 - 4 bedroom house on a 1/4 acre lot starts at $600 in good condition. Prices go up from there depending on neighborhood, condition of the home, school district, etc. A 4 bedroom house in a top rated school district with a nice size yard and move in ready can go as high as $2.5 million. On the flip side, the same exact house in a low income neighborhood with a low rated school district and needs an updated kitchen or bath will sell for $400 - 500K
You will never find prices like these in NYC. First get pre approved by a lender, then start exploring the suburbs and find a realtor to work with. Example: Douglas Elliman who used to be only in Manhattan has moved to the suburbs.