I think you're referring to the City Marina, which is behind a seawall on the Ashley River. Ashley marina is just upriver of the City Marina, on the other side of the bridge. The anchorage is still OK, although you must be aware of the current. There are several sunken boats there and a lot of old semi-abandoned boats at moorings and at anchor. My experience is that the City Marina (which is actually a private marina) does not keep track of who is on moorings in
the Anchorage area. There's usually plenty of room to anchor, although it sometimes gets tight when the snowbirds come through. You can anchor on either side of the bridge.

Charleston Marina (Patriots Point) on the Cooper River near the USS YORKTOWN, is also good. I keep my boat at another Marina, the Cooper River Marina, run by County Parks and Recreation, on the Cooper River at the South end of the old Naval Base. It has good rates, professional, helpful staff, and good facilities. Only drawback is it's location, further from downtown Charleston.