In my final year as a grad student, I interviewed and got a job offer at DEC. At the time, the average starting salary for a new Ph.D. was $58k. When I got an offer for $74k, I was elated! I blurted out to my hiring manager, "That's a lot more than I was expecting!" He laughed and said, "You're not supposed to tell me that!" In my mind, I knew it was terrible from a negotiations standpoint, but I didn't care. I was graduating (finally!) and ready to make money in the working world, and happy to be making much more than average.
If I could go back and talk to my younger self back then, I would say, "You're going to get an offer that's higher than you expect, and it's going to make you very happy. It's OK to say you're happy about getting an offer, but ask if they can go a bit higher. Even if you don't care about the money now, the cumulative gains in the coming years will be huge. Plus, it's always good to practice negotiating in the real world. Good luck!"