2001 Hyundai Elantra - rattle on left side, also bearing type intermittent sound

Could be a strut/shock, sway bar end link on the left . The bearing noise could be idler pulley, tensioner, alternator.

I'm not 100% sure, but the accessory drive on your car might be on that side, the left (driver's side). I would cycle the A/C off (if you had it on) and see if it goes away. If not, lift the hood with it idling and try to hear where it's coming from, generally speaking. Like if it's in the accessory system (aka A/C Compressor, Power Steering Pump, etc.) You could take an automotive stethoscope and put it on the accessories or center-bolts for idler pulleys one by one until you hear the noise. A long screwdriver works too, you can put it up to your ear and put the tip on the pulley, etc. Just be CAREFUL not to get anything, or yourself, caught in the belt drives. That should be a 2 or 3 belt system...Alternately, you could take a belt off at a time starting at the furthest one out and start the car, see if the noise is still there. If so, take the next belt off. When the noise stops, then you'll know which couple accessories it could be. Then you can reach down and spin those one by one by hand and feel for one that feels loose, rough, hard to turn, etc. They should all spin smoothly.

/\ Since I can't edit, I need to say that it won't hurt anything to run the motor for short periods of time without belts on it, but don't let it sit and idle with them off for very long.

CV joints leakin' the poisonous grease, by now~?

honkin' starter bearing....consider which car this is~ not a toyota~