The NY Times calculator is pretty accurate and comprehensive from my experience. I do have my own model in Excel, and I used it to model probably over 100 different listings during 2016. My model tends to be just slightly more aggressive (more likely to recommend Buy) than NY Times’, for some reason that I never figured out. So, it would probably be better to use the more conservative model if this ends up being the case for you. In fact, my wife almost killed me after we looked at so many places for my research, only for me to conclude that I didn’t want to buy anything…
In terms of other variables - you can generally represent that in the NY Times model by adjusting some of the known inputs. For instance, you might have some co-op transfer cost or something, but you would just include that in Closing Costs.
What is not captured in NY Times is the scenario where you keep the property and rent it out later, rather than sell it when you move. This has a huge effect on the results. What makes the “Breakeven Time” analysis, as used in models like this, relevant is the very significant transaction costs of real estate. Given that you will lose 5% to 11% if you sell the property, your economics improve if you hold the property for a long time, since the benefits are amortized over that long time also. However, if you do not sell the property - ever - you save a large amount and the economics move in your favor. You would need to make your own model of cash flows to see how this scenario works for you - the sensitivity to opportunity cost will increase, since the holding period is longer.
Also, don’t take any numbers in your inputs at face value, since property owners have incentive to inflate numbers in their favor. For instance, if they say the rent of some apartment would be $5k, it’s usually lower than that, since many places provide incentives like free month rent to make the figures look good.
In addition, you should add some amount to the Breakeven years in the NY Time result to account for liquidity or mobility premium. If you are economic neutral at 5 years, for instance, it is better to rent, since you can leave at any time. Your money will presumably be in liquid investments like stocks, rather than an illiquid real estate asset. So, you can change your decision easily and with little cost. This option is worth a lot of money.
Anyway… I have lots of things to say about this, having spent 100s of hours looking into NY real estate for my own purposes. Probably is better if I don’t go off topic.