Valley of Fire is amazing. You can also drive out to Techatticup Gold Mine and Nelson, NV, which is a very quirky ghost town. You can visit Rhyolite, Death Valley, the Grand Canyon, Mount Charleston, Bryce Canyon, and Zion National Park. All of these are very easy drives from Las Vegas, though some are longer than others.
Las Vegas sits in the middle of many amazing places to see! No matter which direction you go there is a place of significance. However, most are at least 2 to 3 hours drive. If I had 1 day, I would drive to Zion National Park--leave exceptionally early from Las Vegas to get there and have the whole day to spend there. You can not drive in the park, but there are shuttle buses to all points in the park. Zion is absolutely beautiful!