Ripping apart an old analog radio and mechanically driving the tuning knob would be amusing in an odd retro sort of way. When dealing with a cheap off-the-shelf "normal" radio, the ugly part would probably be trying to hack around the human interface.
Buttons are likely in a matrix configuration, so that's the first "ouch", the second is trying to interpret any user output from something like a LCD - which would be pretty tricky. Probably impossible without having a microcontroller directly parsing the LCD control lines.
Might be easier to splice in/ hack directly into something that resembles a varactor in the tuning section. If there is one - that is.
James