Contrary to popular belief, your base salary is not the only negotiable part of the process.
If your potential employer can’t budge on base salary but you really want to work there, there are other options. Have you considered a signing bonus? Relocation money (if applicable)? Stock options? Or perhaps a week or two of extra vacation is worth a small decrease in base pay. The point is you have a lot you can negotiate in addition to your base salary, and you should tailor it to suit your needs.