Rough idle

When adle the engine
has a bad vibration you can feel the vibration when driving down the road I come home and took the serpentine belt off, started engine up and it ran smooth. That tells me I have a pulley messing up what would be recommended to replace, which pulley.

Welcome to af, from here we cannot diagnose this, most common cause, based on your description, would be the fan clutch is frozen, causing the fan to roar, or one of the belt pulley bearings failing.

If you remove the belt and spin each accessory by hand, it may be revealing. Water pumps and steering pumps are suspects, as well as the other accessories and idlers. Anything bad enough to cause a noticeable vibration should be evident by hand-spinning it.

There is a remove possibility that the AC compressor is failing, but that could be accompanied by noise, and diagnosing would be simply require turning the AC off.