Can't make any suggestions as far as accomodations, but I will say that 'location' isn't as big of an issue on Jekyll as other places. The island is so small that you can literally go from the far south point to the north point in 30 minutes on one of those electric rental cars (suped-up golf cart).
IIRC, there aren't a ton of accomodation choices there - no "beachfront high-rises" like most beach locations. The old 'club' on the inland side seemed pretty cool - lots of history in that area. There were a couple of different restaurants in that area as well.
On the ocean side, I only remember a couple of larger 'resort-ish' establishments - neither of which seemed too 'sketchy'.
Make sure to check out the driftwood beach on the north end. Pretty interesting scenery.