Your starting point is the market average range of salaries for your relevant experience, location and job title.
I would not use your living expenses as a lower limit - frankly they are somewhat irrelevant on their face to a prospective employer. Of course indirectly in order to get people to fill job in expensive markets, they will have to pay more, but its not based on your expenses.
This leads me to the crux of the answer - you need to understand the local market average salary range based on your experience. Specifically years doing this type of job - not total years doing other type of work. You must be confident in what they would pay someone with your same relevant experience.
There are several great resources for this: Salary.com and Glassdoor both have general salary calculators that focus on Job Title and Location. LinkedInlets you add years of experience and also industries to better hone in on salary ranges (a premium subscription is required but if you are job searching this is money very well spent). There are also industry/role specific salary calculators like the one on our sister site Stack Overflow that include degree, years of experience, etc (all for free) specific to developer and IT roles. For a more in-depth salary calculator look at PayScale and be sure to use "evaluate a job offer" option - again you want to be paid for the work you will be doing and not what you do now or in the past.
Once you know your worth here's a strategy for negotiating salary:
If the ranges you find are suitable to your needs (in your case at least $150K), then you should use language like this:
"I am pursuing XYZ job titles in the range of $ABC to $QRS. Based on my experience and market averages for ABC titles in New York, this range is very consistent with market rates."
This establishes that you know what you are worth, you have done homework and it gives you a range of salaries that you would be comfortable making. It takes your personal situation off the table and makes the salary negotiation more fact-based. You are competing against other with similar backgrounds - not your past experience - if you can do a job they should not underpay you because you were underpaid at your previous jobs. If they ask you what you are making now - simply say that your current job isn't really relevant to the kind of work you are seeking and I would prefer to use fair market rates. Assuming we mutually agree this is a good fit, I would imagine prevailing market salaries would be fair to both of us.
Caveat - if you get some incredible bonus or perks or if the job is not a standard industry job these ranges may not work. If you are looking for typical industry jobs these averages will give you confidence to seek what you are worth.
I personally used this approach and it was helpful not only in negotiating my current salary but also for eliminating positions that could not meet my salary range - being transparent saves everyone time and if the data is good (generally I found most of the ranges converged pretty tightly across sites) then it is a fair conversation.