Hyundai Sonata Vibrations

I am guessing that you have never had the tires balanced. As a result, you are feeling vibrations both because the tires are out of balance and also because they are now out of round, so having them balanced will likely NOT solve the problem. To confirm this, do the vibrations seem to come and go a bit, and do these vibrations seem to moderate at higher speeds or when going around curves on the highway? If so, the only remedy likely iis new tires. Just to be sure, get a four wheel alignment and have your current tires balanced. If the problem still persists, then you know that you have proper alignment and simply must replace the tires. Don't continue to drive with the old out of round tires because doing so will prematurely wear the wheel bearings and suspension linkages, and since the old tires are getting far less traction with the road which is inherently dangerous.