My son's dad and I were together five years, and split when he was almost two. We lived in a town of only 2000 people, and I ended up moving to the apartment across the street from him. We continue to be close, and though our parting was best for everyone (including my son), his dad and I are still on good terms and they see each other whenever he's willing. But I know we have an unusual ending to our unhappy story.
Personally, I say the best route is tell your children that even though Mommy and Daddy don't love each other anymore, they are still very loved, and this isn't about them. Make sure they know that it's ok for them to still love both of you, and be supportive of their questions and concerns (my son would routinely ask me if daddy still loved him, or if I was going to take him far away).
As far as where to move to, do what's in your heart for YOU, not out of fear/regret/revenge to your ex. At this point in life it's hard to think of yourself and not just the kids. You need to focus on what you will need to get life to where you want it so you can be happy, which will in turn make your children's lives more happy. I was only 22 at the time of my parting, and had hit literal rock bottom. But the time alone through very hard times showed me that I was strong enough to do this, and I know I'm better for it now. It also made me appreciate what I had, and not whine about what I didn't. I know this was a major factor in my meeting my husband, and has shaped how I've raised my children.
Divorce is a very hard thing for everyone involved, not just the kids. Do what you feel is right for you. As far as discipline, that is something you and he will need to discuss just the two of you. My ex and I usually have weekly phone calls to keep in touch and point out what we want for our son, and make sure we're not saying opposite/contradicting things. Hang in there, stick to your guns, and keep your chin up. I'll be praying for you and your kids.
*~* As for grandma, offering to let her stay once was a kind gesture, after that, she will see it as meddling and will push you further away. Undoubtedly at this point in time, she's feeling very up-in-the-air about things (something very permanent in her life has just disappeared) and she needs to sort through this on her own. Rest assured that when she is ready she will come to you, but she's old enough to make her own decisions, and sink or swim, she needs to do this. My parents watched helplessly as I took wrong turn after wrong turn, but eventually I got it right, learned some hard lessons and have a beautiful family and a very fulfilled life now. I wouldn't have had it without my time alone. Watching our children stumble is heart-wrenching for us, but we need to realize that without the mistakes there can be no success. I wish you the best during this hard time in both your lives. God Bless. *~*