My first thought is a loose or leaking vacuum hose, but surely if the
dealers tech has checked it out they would have found that.

Sonatas with the 2.4 engine have quite a lot of vibration when the car is
in gear.  This is, unfortunately, inherent in their design and will never
go away.

Since you say the vibration has gotten worse since about 27,000 miles,
it's possible that you have an issue with the motor mounts.  If that's the
case, replacing them will reduce (but not eliminate) the vibration.

You could call Hyundai customer assistance, but I'm thinking that won't
get you very far unless you meet with the factory rep and are absolutely
adamant that the vibration is significantly worse than before.  

If you're game, call the service manager and offer that you won't bring
the issue up again if they replace both upper mounts (one engine mount
onthe right side of the vehicle, and one transmission mount on the left).
Of course, this means that if nothing changes, you'll need to keep your
word that you won't bring it up again.  But in that case, I'm suspecting
that the vibration is indeed normal, as they say.

I was told today by the dealership service manager that in was
inherent with the 2.4L engine and that there was nothing more they
could do. I have called the Consumer Affairs to complain about it.
They are to call the dealership and get back to me next week. I will
ask about the motor mounts.
Thanks.

Is there a torque spec on the motor mounts? I wonder if that is my brand new
vibration problem.
(I just had the motor mount out to work on the timing belt. - 01 sonata
2.4l)