The higher the speed rating, S, T, H, and V, generally softer the
compound, and less long-term life (treadwear) of the tire. Properly
inflated and maintained, an S or T rating would be acceptable on an
Elantra. S-rated tires are not as common as they once were - say back
in the late '60s or early '70s - now typically replaced by the T-rated
tires. My SAAB uses T-rated tires, and it has a much higher top speed
than the Elantra. Now, if we were discussing a Sonata with the V6, I
would consider only the H-rated tire as a minimum spec. But, it really
comes down to the point are you even going to drive the Sonata in
excess of 120MPH for long periods of time - I typically don't think so
here in the USA.
More important that the speed rating for the Elantra application is the
DOT UTQG ratings of the tires, as to temperature, traction, and
treadware grades - especially temperature. Buy a S or T speed rated
tire with a "A" temperature grading, and you will be fine for the
Elantra. High temp is the cause of the majority of tire failures, and
this is normally caused by underinflation and overloading.
Keep your tires inflated to proper pressure levels, and all will be
fine with any of the aforementioned speed ratings. After all, the
Elantra is not a Porsche, and using HR or VR rated tires is really
overkill.