I recently got my parents a fanless desktop computer. There a lot of options, but I went with a cheap Shuttle XPC slim barebone [1]: It is tiny, has a really nice industrial design and two front facing COM ports (!).
Yes, I noticed that to. I just ended up going for a cheap ~6 Euro USB adapter. On the plus side you get an SD card reader. (And besides Bluethooth it has great connectivity: 2x LAN + WLAN with external antennas.)
"Two serial ports: Many PCs do not have these legacy ports any longer, since they have been superseded and replaced by USB for most consumer applications, but they are still commonly used for applications such as industrial automation systems, scientific analysis, POS systems and other such fields of application."
[1] http://www.shuttle.eu/fileadmin/resources/download/docs/spec...