Eye_ball

I've always had a hard time leaving home. All through undergrad I would cry most of my drives back to school and that was when I only lived a few hours away. Last summer I moved 11 hours away from home to start my grad program. The first year went really fast and I had a few rough patches, but I made it. Now I'm finishing up what will be the last summer break of my adult life and I'm having a really hard time coping with the fact that I won't be home much these next three years of school. My program becomes year round after the first year is done. All I can think about is how much can happen in that amount of time. My grandparents aren't getting any younger and what if this is the last time I get to see one of them? It will also be the longest amount of time Ive gone being away from home. My next visit will be thanksgiving. I'm just really starting to regret going to school so far away. It also doesn't help that I kind of feel alone at school. I have amazing friends at home and I have amazing friends from undergrad, but I really haven't found anyone who understands me at my new school. I have a hard time showing my emotions to my friends and family because I don't want to make my parents and friends worry about me.  It would be really great to have someone to talk to who is maybe going through a similar situation or to just hear some advice on how to cope with this hard time and these thoughts I've been having.
 

What I like to do is send letters to my grandparents. If your grandparents are more electronically-savvy than mine you can maybe do Skype chats. Regardless, although regular contact doesn't match seeing somebody in person...it is still maintaining a strong connection.
It sounds like mentally you are still living at home. You may need to try harder to live in the place your body is (in this case, grad school). That means making a decent effort to find new friends. Sure they may not "get you" in a way your childhood friends do...but that doesn't mean you can't enjoy their company or form a meaningful connection to them. Part of being "got" involves helping people understand who you are by opening up and being honest, and by making an effort to understand the other person. 
What I liked the most about moving away from home into places where I knew no one was that I had to opportunity to try new things without any obligation to others. For example, when I was living at home I did a lot of long-distance running with a group of people. When I moved an hour down the road to university I continued with the running because I was still connected to that social group. However, moving to a new country meant that I could break that pattern and take up new sports. I kinda found it more fulfilling to form a totally new identity in the foreign country, rather than attempt to continue with my old habits. It helped me make a more meaningful connection to this new location and made the experience feel less transient. If there aren't grad student societies you can join in your school, look on Meetup.com for interest/social groups you can check out.
I know that your family wants you to be happy and productive, wherever you are in the world. Your experience in this new location is whatever you make it!