patio11 is correct. You should always try to come from the frame of you being excited about the opportunity and first want to make sure it's a good fit. The onus isn't on you to give a number, and in fact it's pretty ridiculous for them to demand it. If you've reached the final stages you should be getting an offer letter with a salary amount and then you can negotiate from there. That not happening sounds strange. W…
It is a large company that opened a new office in a different city, but there are no salaries online from positions in this new office. I can get an idea of how much a software engineer at the same company in, say, San Francisco makes, but of course I'll be making less here because of the difference in the cost of living. My default number would be the median salary for a software engineer in my area, but to be hones…
The company's quick alternative is to move someone from another location. Not only is such a person unlikely to take a pay cut based on location, they may ask for more. And certainly will ask for relocation expenses.
Relocation expenses, recruiter fees, etc are all part of the company's budget, not just salary. Don't sell yourself short.
Good luck.