As far as Public Safety agencies go, you can monitor HHI Fire/Rescue on the Palmetto P25 system. All Law Enforcement is encrypted.
You can monitor SCHP and other state agencies on the Palmetto 800 system, program the Bluffton site. You'll also hear Jasper County and Hampton County agencies on that system.
If you're near the water, the marine channels might be a good choice.
If you're in to Mil Air, MCAS Beaufort is fairly close, so you might catch some activity from jets if they're active.
There are plenty of businesses and security agencies active on HHI, but I don't know how many of those are active on analog radio systems anymore. I suspect plenty have migrated to DMR or NXDN systems by now. If you have SDR capabilities, it's probably a rich environment.
I'll be at Hilton Head in just a couple of weeks for a short visit, and I'll report what I hear.