I have the same problem. I purchased my '08 Santa Fe back in December. The deaership has been giving me the runaround. The first time I brought in (Christmas Eve) they balanced the tires, told me they did the road force balance on the Hunter 9000. I've brought it in 3 times since then because the vibration has yet to go away. The 2nd and 3rd time, they did nothing and told me I was imagining the vibration, I can assure you its not my imagination, I've had 3 other people in my vehicle tell me that it is vibrating and it wasn't normal. This last time I told them they need to comply with TSB 08-SS-003, and told them to replace the tires, I also opened up a case with Hyundai. Come to find out the dealership lied when they told me they did the road force balance, they didn't, so Hyundai told them to do it. Apparently, my tires are fine, so according to the TSB they need to replace the tires, they're refusing to do it, telling me that there is no vibration in the vehicle. Needless to say I'll be back on the phone with Hyundai later today.
My suggestion is to first reference the above TSB and tell them to follow through with that. If that doesn't work I've read that there are several other things that could cause the issue, like an unbalanced drive shaft. I'm pushing for the tires to replaced for this reason, my Santa Fe had less than 2 miles on (from driving at the track when it rolled off the assembly line), it was brand new when I bought it, just rolled off the truck and still had all the white protective tape on it. Look on the door and find the manufacture date, mine was in June of 2008, which means the vehicle sat for 6 months without being driven. This can cause flat spots on the tires, this is why when you don't plan on driving a vehicle for an extended period of time, they tell you to put it on a lift. The flat spots on the tires could cause a vibration similar to an unbalanced tire. Check your manufacture date, that might give you a hint, seeing you just purchased it, I would be willing to bet your vehicle, like mine, sat for 6+ months before you received it.
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