Jack up the front end. Wiggle the front wheels up and down and side to side to see if there is any looseness. This could indicate ball joints or bearing wearing out. Check all of the tires for any bubbles, uneven wear, separation, missing weight, or bad spot. Rotate the wheels front to back so that you can see if the vibration moves from front to back. While the tires are off, check them more carefully for any damage. If you still can't figure it out, try having the wheels rebalanced.
2001 F350 XLT 4X4 crew cab, dual rear wheels, long bed, black, 7.3l turbo diesel, automatic transmission, 4.10, shift on the fly, running boards, sliding rear window, 38 gal fuel tank, Odyssey extreme 65-PC1750T batteries, Michelin LTX-MS2 rear tires, Sumitomo Encounter front tires, Shell Rotella Ultra elc, 11,500 gvwr, 20,000 gcwr, 7500 gvw, completely stock, 114,000 miles when purchased, now has 250,000 miles, repairs so far: two starters, batteries, cps, brakes, tires, alternator, ball joints, locking hub, wheel hub, AC compressor, serpentine belt, power steering pump, driver's side window, ignition switch, o-ring, Spectra premium radiator, water pump, fan clutch, fan blades, thermostat, thermostat housing, tensioner. Stolen twice so far, but recovered both times with major damage.
2005 Nomad Rampage toyhauler made by Skyline. 11,500lb gvwr.