Could be a number of things. Off the top of my head:
You mentioned "grinding". You could raise the car and check play at the hubs (try to wiggle the wheel back and forth, up and down). Does it make a grinding noise when you turn a corner? If so, that's a symptom of worn out front bearings.
Check the condition of the ball joints (if the dust caps are shot, the joints are probably not in great shape, depending on how long the caps have been gone) and the various rubber parts (e.g., strut rod bushings).
None of these rods/joints/parts should be loose.
Wheel balance is a common cause, as theterminator93 pointed out. Not much you can do to check that yourself w/o a balancing machine of some sort (most shops use computer spin balance these days).
That said, there are some things you can check. Look for thrown/missing balance weights. If you see no weight on a wheel (check inside the rims if that's where you had the shop put them) but there are scratch marks on the wheel, a weight was probably formerly there. Of course, the weights and their positions can change, sometimes dramatically, when you change tires. It's rare that a tire/wheel combo is perfectly balanced and will thus need some kind of weight somewhere. If you have no weight on a wheel, that wheel is probably out of balance.
Also, check your tire pressures and make sure they're at the same pressure the tire shop had them at -- you can have an out-of-balance situation with incorrect pressure.
Could be loose/worn steering components or linkage. Check the inner and outer tie rod ends for play. They should be tight. Try to wiggle the steering column all the way from the steering wheel down to the rack. There should be no play.
There could be a fault in the rack and/or pump which is causing pulsations.
Also, just because rotors are new (or turned) doesn't mean they can't be warped/warping. If you get shimmy which is worse while breaking, you could have warped rotors. Raise the car and have someone lightly engage the brakes as you turn the wheels. If the rotors are badly warped, you'll see/feel the difference as the wheel spins.
edit: most of the above relates to steering wheel vibration. I now realize that you are probably referring to entire chassis vibration. You can experience this if something is amiss in the rear, also, it doesn't necessarily have to be a front end problem. Check rear bearing for looseness. Check rear suspension components for play, loose bolts, etc. Check driveshaft for play. Check transmission mounts. As you can see, a great many things can cause chassis-wide vibration.
Last edited by Torque; 06-16-2012 at 07:25 AM.