If you are looking for mellow terrain around Shrine, you should continue on the 10th Mountain trail as if you were heading towards the Fowler/Hilliard Hut. The trail goes past Chucks and Walters cabins and heads south/southwest. The trail will take you across a wide open hill just past Walters Cabin that is some very easy skiing that your family should like. If you want more challenging and the snow is fresh and not all wind blown, you could continue up the trail to the top of Shrine Mountain and ski some of the western facing terrain from the ridge or just west of the summit (consult your map on this).
Another place that is really good is Black Lakes Ridge. Go back out the way you came in and stay on the road back towards Vail Pass. You dont have to go far to a saddle and if you ski to the left after reaching that saddle, you will find some really good east facing bowls, slopes and trees. Fun for all but you have to skin back up after skiing and some people dont seem to like ending their fun with an uphill. Again, consult your official 10th Mountain map so you can find these areas.
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