While it has been a little while since I left boot camp, the way it worked when I was in was that depending on where you were in your training time, you may or may not ship out to Charleston immediately after Graduation. For instance my division along with 13 others graduated on a Friday, we had liberty weekend and didn't "ship out" until the next thursday. We were at the tail end of the graduation class. Other divisions that were towards the front of the graduation class shipped out anywhere from immediately after graduation all the way until the next Friday(1 week). Pretty much whatever you brought with you to boot that didn't have to get shipped back(shoes, personal small items like watch, glasses, etc) and the stuff they issued you is all you had when you went to Charleston. Civilian clothes are superflous since you can't wear civies until much later in the training pipeline, and by then you have had a chance to go to the mall and get some new threads. Of course this is about 9 years old so things have probably changed some.
Their may not be much in the way of biking in Charleston, but there is an abundance of other things to take in. Paintball(great field down there, lots of players), ice skating, downtown, beach, golf, short stay(if you are allowed to go), etc, etc. You can always have things shipped to you, or well you gotta have someway to spend all that big money you are making now, NUB.