Your first stop should be the visitor's center. They have a very good display and explanation of history in the park. Something I did not know was that Valley of Fire was Nevada's first state park.
At the visitor center there is a very good book and gift shop. You can also get water here for your hikes which is important.
After visiting Atlatl rock, continue driving around towards the Arch Rock Campground. On the left this is Arch Rock. There is no real parking area to view the arch, just a few pull offs so be careful if you get out to take a picture.
Some of the best petroglyphs in the park are found at Atlatl rock. Interestingly, the name is from and ancient piece of wood that was used to throw darts for hunting. There is a steep walk up some stairs but it is right from the parking area. Also, there is protective plastic and fencing due to some obvious vandalism. It is a shame people felt the need to scratch and deface this ancient history.
This is a short little trail just off the Valley of Fire Highway, near the west entrance station. A very easy walk with a few "logs" visible. The logs have a protective fence around them but easily seen. If you've never seen petrified wood before its a nice walk to check out. If you have seen it before, probably just skip.
This is a very easy hike right next to the visitor center. The trail maker states it is .5 miles. No way. More like .3 miles round trip. Very easy. Be sure to walk past the spire and turn around. You will get a much better sense of how the rock in balancing.
You could spend weeks out here, there is so much to see! I would recommend going October-April, when temperatures are cooler because it can be unbearably hot in the summer (40-50ºC) and bring lots of water. You can drive the roads through the park and stop and get out where you want, but you miss way too much in my opinion to go about it that way. There are all kinds of things to see here, petroglyphs, red rocks, petrified wood....
The last stop along the main road. This is another of the iconic formations of the park. There is no parking right by the rock, and stopping here is a bad idea (it's near the crest of a hill.) So, you need to park at the East entrance station, and hike back to the rock. There's a trail from the station that heads slightly north and around the back of the formation, or you can jump on the scenic road and hoof it up the couple hundred yards. If you take the trail, you can also see the countryside in the vicinity of Elephant Rock. This was the last trail I took, and it had some modest elevation changes and mild scrambles. Perhaps since it was the last trail of the day and I was tired, I wasn't as impressed with the scenery on this trail. I did catch a glimpse of a coyote or wolf running away from me at one point. I would definitely recommend the hike to Elephant Rock, but am less inclined to recommend the rest of the trail.
You reach the Cabins by following yet another short spur road off to the north. At the end of the road, there are a set of historic stone cabins built with the native sandstone of the park by the Civilian Conservation Corps in the 1930's in order to provide shelter for travelers in the area. A very neat set of buildings. As I was leaving, a wedding was setting up shop nearby to use the area as their backdrop. One word of warning - this was one of the few spots where parking was quite tight, I almost got boxed in by another car who also wanted to stop and check the site out.
Seven sisters really doesn't hold a candle to many of the other areas I saw in the park. You can pull off the road to see these large formations, and if you walk around the backside, you are treated to a expansive desert vista. Between the formations of Seven Sisters, there are a number of picnic tables that are set up for people to enjoy a meal they may have brought with them. There are portable toilets at this stop, but indoor plumbing is available 5 minutes away at the visitor center. I did happen to hit this stop at a time when the sun did turn the rocks into a firey red though!
Right outside the visitor center lies another one of the famous formations that you'll find in the park. Valley of Fire seems to have a little of everything - arches, painted rocks, petrified wood, and balanced rocks. From the visitor center, you can take a very short hike to a viewpoint of Balanced Rock, or, as you are coming back down the scenic drive, if there's nobody else on the road (I was lucky to have this scenario), you can just stop the car and get a good look at this formation.
Just over 5 miles from the visitor center, the White Domes area is the last stop on this leg of the park. Much like the Rainbow vista area, there are a lot of contrasting and beautiful colors to the rock formations in the area, making this another impressive stop. This stop also has a one mile loop trail that you can take to get closer to some of the formations. The trail has some tricks to it - there are elevation changes and rock scrambles involved, as well as the opportunity to squeeze through a slot canyon. There also is the site where the film "The Professionals" was filmed in the 60's has left a few remains. You return back to the parking lot passing a few more nifty rock formations. Definitely worth your time to take this hike!
Off the main road, you can take a short dirt spur road to a small parking lot with a nice set of vista views. From this point, you can see the red Fire Canyon (which I also saw on the hike at Rainbow Vista) and you also can see the impressive Silica Dome. There are trails from the parking lot to these features, but having mildly wiped myself out on the previous hike, I decided not to take either. The views are quite nice, making this an easy decision to do the side trip to see them.
The next stop is at Rainbow Vista. The park brochure claims this is a favorite photo point due to the various colorful sandstone formations in the area. I decided to walk a trail here out into the desert for some more scenery. The trail is well marked with a number of signs. Eventually, you can decide to loop back to the parking lot (total distance was under a half mile) or continue down a gully to a view of Fire Canyon. I took the spur trail to the canyon. This trail was a little trickier - it wasn't as well marked (although you really can't get lost since it is in a small canyon), and I had to do a few scrambles down and up. At the end, there is a payoff with a nice view of Fire Canyon. Then, it's back the way you came, and finish off the original trail back to the parking lot. Note, I was alone almost the entire trip, a great place for you and your thoughts...
Heading north from the Visitors Center, there are a number of interesting stops. The first is Mouse's Tank, which is named for a scoundrel who used the area as a hideout. The tank is a natural basin where rainwater collects and remains for periods of time. It's the only place I saw water in the entire park! To get there, you walk a trail through a gully - round trip, it's about a half mile, and although the trail is pretty flat, it's quite rocky so you need to watch your step. You still need to take your time and look up every once in a while - some of the rock formations surrounding the trail are pretty neat, and you also will find some petroglyphs on the walls if you keep your eyes out for them.
Continuing east, the next small gravel offshoot from the main road leads you to the Petrified Logs. As you leave the parking lot, you can take a loop trail to see these logs. This trail has some minor elevation changes to it, but nothing too difficult. I took the path counterclockwise, which meant the first part of the trail was more general views of the peaks, valleys, and other formations of the park. The logs came on the second half of the trail. They are all fenced in, to prevent souvenir hunters from depleting these few treasures. The forest these came from are estimated to have lived 225 million years ago.