As of the February 2010 phonebook, Palmetto Fine Cleaners had four locations listed while in the 2011 phonebook there were none. I've done one of the Broad River Road locations, but this one caught my eye last week while I was heading to lunch at Grecian Gardens (and to take some pictures of the Sunset Boulevard Fred's location).
I have to say it's an attractive little shop -- I like the Palmetto logo, both on the marquee and the back wall, and the little flower archway is a nice touch (though I'm not sure how it fit in originally).
I'll also note that when I did the closing on Burnette's Cleaners at the other end of this plaza (but with the same 2250 address) I said in error that Palmetto had been in its spot. That's what relying on googling a street address (and not driving the full length of a strip mall) will get you.