Yeah, you’ve got the general idea. The prevailing wisdom is that rent always goes up, and a mortgage caps how much you could pay (aside from taxes).
Sounds fantastic! You certainly won’t regret those savings even if you choose not to buy.
Up to you and how much you want a house. The way you write, it sounds like you feel obligated to buy and you’re not passionate about it, so I recommend continuing your aggressive strategy and consider dumping the down-payment money into a brokerage account.
I have never been to NYC, so I have no insight here.
One thing you should consider is total value of investing vs buying a property. Stocks should return something like 7% after inflation, so you’d need to estimate:
how much rent will increase - can look at past data to get a feel for averages
how much the property would appreciate - NYC is weird here
how much you’d “waste” in interest, taxes, etc vs how much goes to principal; compare vs the amount you’d save w/ rent
It could very well turn out that renting is the better financial decision, and that dumping money into stocks can help fight the increase in rent prices. I know NYC real estate is messed up, and that includes both buying and renting properties. So while you’re saving up the down payment, I recommend running numbers to compare buying vs not buying and continuing to save. Basically, estimate your net worth after 30 years or whatever if you buy a house vs invest. Then decide what lifestyle you’d like, and how that fits with the numbers.
In my case, we wanted a house and we found a good deal, so buying made a ton of sense. Then again, I live in the suburbs in a semi-rural area that’s growing quickly, which is a very different situation vs NYC. If I were to move to NYC, I’d run those numbers before assuming buying is going to be the better choice long term.