I have "seriously dated" three women. The first, I dated for about 9 months in college, but it was really just a break-the-ice-on-having-my-first-girlfriend relationship, and she broke it off towards the end of our senior year. The second, I dated for about three years and for a time expected that I would marry her, but I eventually broke it off. After a couple years of only casual dating, I hit the jackpot with contestant #3, we dated for three years, got engaged, and are coming up on one year married.
The breakup from #2 was rough. I'd been with her for two-plus years and marriage was on the table. Some of your reasons are quite similar to mine, although the biggest reason I broke it off was some friction between my GF and family that I felt was my GF's fault, and it was gnawing at me that as hard as my mom and dad tried, my GF just didn't seem like she would ever warm to them. We also had some different feelings on a few other issues, and eventually I decided that we should end it.
There were some sleepless nights in the week before, and a few more in the week after. For the next couple weekends, I was definitely in a bit of a funk...I had some weird Saturdays where I went to the grocery store in the morning, worked out...and then went back to the grocery store in the afternoon because I was so bored (I mean, for a couple of years I'd spent every weekend with my girlfriend...and suddenly that disappeared, what was I gonna do?)
The best thing I did to break out of the funk was...do stuff. I reconnected with some old friends from a local running group and started running with them again. I started going to my local yoga studio and actually talked to people. I started hanging out with my graduate school classmates, people who were super cool that I had never really spent "social time" with before I needed to, and suddenly realized how much fun they were.
Chin up, hoss. You'll get through it. The next few weeks will have their share of bummer days, for sure, and you'll probably doubt yourself and maybe even have the occasional "I've made a mistake and should call her" feeling. But if you're about to move across the country for graduate school, you have a fresh start anyway. When you get there, do stuff. Join a gym or running club or hiking group or softball team or frisbee club, whatever floats your boat. Get to know some of your classmates. The "hole in your heart" that you probably feel right now won't go away in two days; you're a decent guy, you feel a little bad about this, it's okay to hurt a little. Give yourself permission to feel like crap...a little bit, but don't get stuck there.
As for when you should start dating again, everyone handles that differently. I would not actively seek out a new paramour for a little while, but if something comes along and you want to give it a shot, go ahead. Just make sure you give yourself a little space before you dive back in.