Red Rock is nice, and is pretty close. You can do the park and get back to gambling ,all in about three hours. I believe the fee is a bit more than $5 though, and they stop collecting it at 4:30, so a late afternoon trip is free.
The Valley of Fire is a much larger park, about 45 minutes north of Vegas.
Between the size of the park, and the longer drive, it's pretty much a most of the day expedition. Be sure to use the Western entrance. For reasons that are unclear to me, it is twice as much to enter from the less travelled Eastern entrance. When exiting, follow the signs for North Las Vegas or you'll end up out by Lake Meade.
While both are nice, if it was one or the other I'd go VOF.
If you drive out to the Dam, leave some time for exploring and shopping in boulder City. It's a truly eclectic place that most tourists simply pass thru.
For me, no Vegas trip is complete without a stop at the Double Down Saloon. You just never know who is going to be playing there, and their "ass juice" is a thing of legend.