Finding a long-term, month-to-month type RV site?

Suggest you try Lake Aire in Hollywood, SC which is just outside the Charleston city limits. Very nice small park with amenities. They have a section where they have longer term residents. Good Luck!

If you do not require park-provided "amenities" like bathhouses and showers, then you might want to look at mobile home parks. These are best for stays of 6 months or longer. You would probably need to put some of the utilities in your own name (electric, cable/internet, etc)

I stayed at the KOA in Ladson

One of the first things the park will ask you, is how long is your rig? Hopefully you'll have an idea as to about how long of an RV you will be getting, so you can help them find the right spot for you. You can do a Google Maps search for RV parks, or use the Good Sam's trip planner tool, or RV Trip Wizard. They will have links to websites for the parks in your area, and you can look at those to find the parks that offer long term rates.