I stayed at the Peppermill three years ago and it was great! We stayed in the tower and the rooms were comfortable and large. I found the casinos better than most and there are several restaurants to choose from. I am going this year and the Peppermill will be the hotel I choose.
Six years ago, I stayed at the Reno Hilton, which is another fine choice but this hotel is isolated from everything else (it seemed like it was out in the middle of nowhere) and the staff was not as friendly as the Peppermill.
BTW - All of the hotels in Reno provide shuttles to and from the airport as well as to and from the Stadium, so do not be swayed one way or the other if a hotel claims this.