I'm at the Atlantis right now, this place is better than I thought (I usually stay at the Silver Legacy when in Reno). It's about a 10 minute drive to the stadium on Virginia St., depending on the traffic. The only reason I'm here is a friend of mine, who is a travel agent, got me the best deal here when I was ready to book the trip. I would come back, I like it.
The Peppermill doesn't look like it has any construction going on. Friends of mine are in the El Dorado, and are happy there. It looks like all the major hotels have shuttles to the stadium, so you don't have to rent a car if you don't want...and of course, several are in walking distance to the stadium anyhow.
The Silver Legacy sports book & bar is definitely the place to be to watch March Madness...great time.