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 honest, I'm a more valuable employee than the average engineer in my area, and think that after this lengthy interview process, my prospective employer agrees.

I've been in the awkward "I need a number situation" and have missed out on a lot of money because of it. One time, I even gave $X, and my interviewer came back with $X - ($X * 0.05). After a month of working at this place, I realized that I could have asked for twice as much money.