Any of the SDR radios will have tuning and recording built into the interface.
Alternately having your audio output patched into a computer audio card, there are many free recording options that can be timed using the computer interface.
Many radios these days have a 'tape out' jack that will work just fine. As N0NHP correctly points out there are many recording packages out there that can be used to record. Learn how to use the task scheduler in Windows and you're all set. We have a few such packages - no doubt there are many others - linked here (blue text is a link)
In defense of my comments above, I assumed the OP was looking for a standalone radio, not something hooked to a computer. The ATS-818 and the Radio Shack equivalent are long gone, and IMHO the wide band R20 is poor on HF for a host of reasons not worth going into here.
Perhaps if the OP has a smartphone or tablet with WiFi, consider buying Tunein Radio Pro http://tunein.com/ for a couple of dollars. The pro version gives one access to international broadcasters and will record audio. You can check out the station lineup on their Web site. I have used the Windows version for years, on a tablet and phone for ~4 years, and am a satisfied user.