My criteria? I just wanted to share that I’ve had good success with MY car. :rolleyes:
That goes in IMHO.
Check and see if the parking (emergency brake) is releasing all the way. Common if you don’t use it regularly or live where salt is used on roads in the winter. If not it can heat up the rear rotors and cause a vibration.
Just wanted to relay my experience with the similar vibration issues. My 05 Elantra would start shaking around 60 mph and taper off above 80. For reference my Elantra started slightly shaking around 75K miles, and slowly increased as I approached 100K miles.
Originally thought it was tires, but after trying two different sets and Road-Force balancing it was absolutely ruled out. Replaced the shocks, motor mounts, left front CV axle (boot started to crack), did alignment, inspected all ball joints (control arms, sway bars, etc.), and even replaced the brakes & calipers with no change.
This weekend, as a last ditch, I decided to replace the right side (passenger) CV axle, even though the boots were still intact and it wasn’t making any strange noises (as a bad CV joint will do). Well that did the trick. The vibration is gone.
Never had a CV axle go bad like that before. The balancing weights were still even in place. The only thing I noticed upon close inspection was that there was a slight amount of play in the inner joint of the axle, and that some grease was just starting to weep out from under the large end of the boot where it is clamped/strapped to the axle. 
I’m not upset about all the other work that was done since with 100K miles, it was time for most of those maintenance items to be replaced anyway. 
So my advice to anyone that is having the same issue would be to check out the CV axles if you have already ruled out the tires, shocks, ball joints, etc.
Great news!
I was working on my daughter-in-laws 2007 Elantra with 125K miles last week. (Earlier I said 2008 with 90K miles - I was mistaken.) Anyway sounds like something is whining on the right front at speed. I was thinking maybe wheel bearing, but I’ll certainly keep in mind your experience with the axle. No vibrations year though.