Hyundai has a 100k or ten year warranty which ever comes first.
This is for first owners.
Your car is over 100k miles ... it is over the warranty period
Timing belt on Elantra ...
If you do the work yourself then maybe around 200 dollars for belt, water pump, idler, pulley, tensioner
(cheaper on the internet)
If you have the work done at a reputable mechanic then 500 to 800 depending where you are