Here's some great advice I got once from my friend Michael Tompkins. I've found this advice very useful and have passed it around to many friends.
Keep the ball in their court.
Tell them that you came to the interview because you were interested in learning about the job and the people. Go on saying that if they want to hire you and you feel like what they are offering is a fit, you're confident that you'll be able to come to a reasonable agreement.
Most people low-ball themselves because they don't want to seem greedy. You are very vulnerable that early in the process, so giving them a number before it's clear how much they want you can only help them and hurt you. Make them put an offer on the table. They'll feel pressure to make a competitive offer. They will not want to offend you. They won't want to lose you because a competitor offers you much more. Plus, they'll know how you should fit into their salary scale based on your experience and qualifications.
If that first offer isn't what you expect, you need to remember one thing. By the time they've made that first offer, they've made a pretty significant effort and they are committed to trying to bring you on board. The hard part is to appear humble and gracious while prodding them for more money. Say you're really excited about the work that they do and the prospect of working with their team, but then explain that you're hesitating to accept the offer because of concern X (and maybe Y and Z). None of your concerns should be that "I know other similarly qualified people that make more" or "I'm worth at least $XXX,XXX." Instead, use housing costs or some other factor that's beyond your control. If their first offer was at the top of the bracket that you fit in under their salary scheme, they'll let you know. If they really want you and they have some latitude, they'll come back with a more aggressive offer. Either way, you won't be taking their first offer off the table and they can't come away with explicit evidence that you're greedy.
Wherever you end up, make sure that the company has room for you to grow and learn. That's really important early in your career. If two opportunities come up, it'd be worth making significantly less and take the job with more growth potential. You'll come out ahead in
the long run.