Ok, I just graduated high school and enlisted. I ship out for OSUT July 5th. I would like to think I'm in pretty good shape. I run 3-4 miles every day (my time for the mile is 6:37) and do pushup, situps, and bench and curl everyother night. Is there anything else I can do to get in better shape for Basic?

In my opinion basic is more mental strength than physical strength and it just shows you that you can do a lot more things than you think you could do. I am sure you will be fine in the physical sense, just dont let the drill sergeants get into your head and it will be over in no time and you will appreciate all the yelling and screaming they do to you...

When i first came in i could barely run a mile in 8 minutes...

Get promoted to E2. Talk to your recruiter and tell him you want to do the pre basic task list. this is what it is:
Pre-basic task list