Technically you could, states still have on the books statutes making sex illegal if the people aren't married, but I suspect any attempt to enforce them would a)make the cops and the town look like absolute morons and b)the law would be invalidated by appeals court if the person somehow was found guilty. However, it wasn't all that long ago that these laws were still enforced, cops in NJ at late as the 1950's used to raid the 'hot sheet' motels along route 4 in NJ and other places, looking for unmarried couples in bed together. There is a famous mug shot of Frank Sinatra from the 1930's, caught in such a raid......
I think prostitution should be legal, for many reasons. In China, I wouldn't be surprised in a couple of years if it doesn't become legal, with the state running the brothels. Recently they passed laws in China, supposedly to crack down on porn, that basically made it illegal to sell porn unless you are a state run media outlet of some sort, state run bookstore, website, etc...guess they figured out it was profitable,and being China, wants no competition with the government..either that, or the places distributing porn/websites/etc, weren't paying enough graft to the government.