what's the cheapest device that will run itunes and connect via USB to a hard drive?

No but a HD tethered would, read my post.. A SSD drive.. wouldn't even slow down.. Second, it's not a gift it's called "PIRACY" If you keep and original.. plain and simple..

Them's the rules feller?? Yuk Yuk.. 

Third an android Galaxy is NOT cheap.. BUT there are a lot of them out there, for 5-20.00 bucks.. Inexpensive at this time in their electronics life span..

4th you asked for the CHEAPEST device. Maybe some one will give you one, in your case throw one at you.. LOL

thanks! the HD of music I want to gift is 700+GB, so I don't think a (cheap) phone would have that kind of storage.

Throw away cell phone? That has a place for a memory card. You can load it via the charge port/ usb or hard connect for SSD and higher speed vs a physical HD.. Would that work? Some of the old Galaxies had pretty beefy processors, too. LOL More than what they had to get on the moon with.. I hope it will play a song, uncompressed.

Regards