There is 1/8” - 1/4” of play in the steering wheel.The dealership said they couldn’t find the problem. What could be causing this and is it an expensive fix?
Could be several things. I will note that you told us nothing about the Suburban except the year. Is it 4wd? 1500? or 2500? Mileage?
Depends on what you think is expensive.
The dealer has failed to find the problem and they had the vehicle in front of them. IF this truck is a 1500, it has rack and pinion steering so diagnosing it shouldn’t be rocket science. The rack coupling, the inner and outer tie rod ends, the ball joints, the wheel bearings, the tires and the alignment all could play a part. If it is a 2500, it has recirculating ball steering and the parts are different from the steering wheel to the knucles.
IF the dealership was competent, the only thing they can’t really diagnose is a tire problem. I’d start there. Have the tires rotated front to back and see if that has any effect. If it does, replace the tires that used to be on the front at the least. Best to do all 4. If that doesn’t fix it, then the dealership wasn’t that competent so find a good independent shop. Preferably a suspension specialist.
First, this is not a tire problem.
Second, 1/8" to 1/4" play is pretty small - and perhaps that is why the dealer didn’t find a problem - because they are looking for something excessive.
But if you are intent on fixing this, start by making sure the tire pressures are according to the vehicle tire placard (It’s on the driver’s door frame.), Then get an alignment and make sure everything is within the inner half of the tolerance. Perhaps the alignment tech will find something.