Once you measure the amperage draw, a few (1-5) milliamps is normal, as radios normally need a little to keep their memory, but if you measure a draw more than that then you got something on that should not be. Bulbs are typical culprits and draw usually 1/2 to 3 amps, for the small bulbs (you would have noticed the headlamps of course). Suspects include broken bulbs and those bulbs that are hidden like in glovebox, trunk, engine compartment, and others like dome, and other interior lights that are supposed to be out when not in use, the automatic switches not being actuated or are faulty.
The next thing to try is pulling fuses one at a time and rechecking the current draw to locate the circuit the draw is in, if the visual is not working. Draw with drop to normal when found. If draw is under 3 amps start with lighting and stereo circuits, if higher the check the larger draw circuits like heater and big stereo systems
Good luck, may take a few minutes or hours.