I would stay in Ketchum instead of Sun Valley. The only thing in Sun Valley is the Lodge, everything else is in Ketchum. Also You will probably be best off staying in what we call West Ketchum. Pennay's is about as close as you can get to the mountain. You can basically ski in and out of the place. And I second that Alan is cool.http://www.premier-sunvalley.com/resort.php/SUN_VALLEY
Here is another site to try for booking a place. They should be able to put you in a place that you will like. Tell them what you want and how much you want to spend and they will do their best to set you up.
January is a good time to come because it is not all that crowded. Not that it is ever really crowded here. If you can, make sure that you ski at least one weekday. You will have the runs to yourself.