If the tires are good, I would support the vehicle on a lift and engage the rear axle. With a mechanics stethescope, you could move the tube to different locations around the axle to identify where the nose might be coming from. Rear end nosies are usually due to outer bearings, carrier bearings, or a ring & pinion that has frosted or pitted.
Many times I will replace the fluid first, and see if that eliminates any nosies due to lack of friction reduction in the gear oil. I always recommend synthetic gear oil.