Rather famous is the Kizlaragasi Han (the "Eunuch's Han" and not as I first thought "Han of the girls with a tree") built 1744, restored 1995. Very touristy, but not bad.
Yep, I knew the -ci adjective (or whatever we call it) indicating a job-like relationship (and much more, I know, I know, I have Lewis's Turkish Grammar, but have been too busy with my site to do much studying), sorry for that. I'll correct it accordingly.
Just a linguistic correction... Tree of girls would be written as kizlaragaci but not kizlaragasi. Kizlaragasi would literally mean master/keeper of the girls, most probably a better translation would be eunuch.