What are the costs to replace the engine mounts on 2009 Toyota Avalon

Mounts may not be the cause of vibration. Try the Estimator tool on RepairPal for relative cost expectations near you: https://repairpal.com/estimator

It seems there is some knee jerk diagnosis happening here. You may want to have another repair facility / mechanic give a second opinion on the urgency of these repairs - or if needed at all. Good luck!