By searching, I've highlighted the string that I want to change.  Now I want to replace only the highlighted text. I'm using n to advance to the next instance of the search string. I was thinking I could do something like ciw but that changes the whole word not just the highlighted text. I'm familiar with :%s/old/new/g but I don't want to change all instances. Instead, I want to advance my cursor to each instance and then decide whether to change it.
How to selectively change a hightlighted string?
search;replace
Use the gn motion to edit the current search match. The following example will change the current match to FooBar:cgnFooBarThe great part about this technique is that you can repeat the change via .. Assuming the next match will be changed the same way you can just use . to repeat. Or skip a few matches via n and then use ..Vimcasts has a nice episode on this matter: Operating on search matches using gnFor more help see::h gn