Of the 3 listed, I would recommend LRO. I have been to both CHS and LRO. Never went to JZI because fuel prices there are typically on par with CHS. If our clients were going to pay that much, they'd rather go to the big airport.
When I was flying corporate, we used to fly to CHS a ton. It's not a bad airport, but if you get your timing off and happen to be wanting to depart at the same time 2 C-17s are in the pattern doing touch and goes and there are airlines in the que as well...you could easily be sitting for 15 minutes waiting to get out. It's still fairly warm down there in September, so unless you have AC, that can be kind of miserable.
LRO on the other hand is a very easy in and out and decent small field FBO. Fuel is also the cheapest of the 3. Only downside of LRO is if you are staying downtown, it is the longest drive of the 3.