I would only stay 2 nights with a 14 year old. Despite Vegas attempting to convince the consumer several years back that it was a "family" destination, it is not. The Bellagio will not let anyone in the hotel that is under 18 if they are not staying there.
We went to Las Vegas with our sons (14 and 16) in March. We were there 5 days and 5 nights. We went to Hoover Dam one day and Red Rock Canyon another day and it was still about one day too many. If your only sightseeing out of the area will be Hoover Dam I would say 3 days would be plenty.
Guest
I agree with the advice you're getting: three days/two nights is plenty for Las Vegas; particularly with your 14-year-old. Come to think of it, it's always been plenty for ME, too. 
