Having gone to Utah in February, I can attest to Alta having some really nice Intermediate off-piste areas, like Ballroom, and some short marked as "expert" areas that an intermediate can handle like Cecret Saddle. Remembering back to my trip to Tahoe a couple of years ago, I can say that Heavenly has some tree skiing and off-piste stuff for Intermediates and there is even some skiable by intermediates stuff at Squaw and Kirkwood in Lake Tahoe. Off-piste terrain is the majority of terrain at many Western ski areas, so finding stuff out West at a moderate pitch that is off-piste isn't as hard as back East.
Back East in the Mid-Atlantic ski areas, a couple of areas leave an intermediate run bump-up to become a mogul field. Liberty, the resort I'm the ambassador for does this. While marked as black diamond, a lot of the ungroomed terrain at Canaan Valley in WV can be tackled by a solid intermediate skier. Pearly Glades at Timberline in WV has a fairly flat pitch and easy bail outs to a groomed run is again a black diamond on the trail map, but skiable by an intermediate adventurous enough to try WV tree skiing. I'm sure there are some New England areas that have similar terrain.