There is no one best itinerary for a day with a 4x4, but here is a copy of my usual post on your options:
There are many off-road sites to visit with a 4x4 Jeep on Lana’i. Here is a summary:
Shipwreck beach is pretty cool. Yes, there is a shipwreck that is easily visible; in fact you can see it as you drive down the long curvy paved road. Where the paved road ends, if you go to the left, there is a sandy dirt road that ends in a parking lot. There are suppose to be petroglyphs near where you park, but I have never found them. The beach is seemingly endless, but takes about 15-20 minutes to get from the parking area to in front of the shipwreck. The beach continues around the island for miles all the way to Polihu'a Beach, but I would just walk out to the shipwreck. In the winter it is can be very windy here, so it may not be the best place for a long hike. I have been told it is much calmer in the summer. There are often turtles in this area. The place where you park is only a few minutes down the dirt/sand road to the left off the paved road.
Where the paved road ends, if you go to straight/right instead, it takes you toward Lopa Beach. This road can occasionally get washed out, but they will tell you when you rent the Jeep. Otherwise this is a rather smooth road and easy to drive. There is one big hill to climb, “white rock”, and immediately after you come over this, there is a turnout to the left which brings you to a nice picnic spot. You will also have to stop at the remains of the old church (there are plans to restore this, and this may be going on now). And at Lopa Beach there is a picnic table and generally calm winds and low surf. It is a nice place to wade out into the water, and turtles can be found here. The road continues to and ends at Naha, another pretty and quiet location. I have never seen anyone at Lopa, but occasionally see some locals at Naha.
You could finish you day up by driving the Munro Trail as long as it is drivable (and since 2011, it is officially “closed”, meaning that the road is no longer being maintained. So check with the Jeep rental company on their current restrictions) . There are wonderful views in various directions and this take you to the highest point on the island. It is a fun drive too; I think about 12 miles of multiple curves and ups and downs. You may be able to see four other islands from the various views. I suggest you finish with this since the end of the road takes you to the top of the hill on the way down to Manele to end your day.
I think going through Garden of the Gods (a very beautiful rocky landscape in a very unusual way) would be another good choice. On the way there you go thru some interesting ironwood groves. There is also has been a short self guided nature tour showing some native Lana'i vegetation right before GOTGs, but this is currently being restored. After GOTGs, the road gets rougher and heads downhill to Polihu'a Beach. This beach can also be windy especially in the winter, but is so big and beautiful that it is worth the drive. It is the size of several football fields and you may be the only ones there. You will see Moloka'i from there and on a clear day maybe Oahu. Because the colors in GOTGs can be very beautiful near dusk, you may one do to this drive last instead. But because of some rough spots in the road I wouldn't drive this back AFTER dark.
Another option is to drive to Kaunolu, another interesting place, and my current favorite spot to explore. But you may have to give up some place else to do this, since it could easily take 3 hours to drive to and explore the area. The road to Kaunolu, the summer fishing home for Kamehameha the Great, is usually drivable, but as of 2012 is reported to be pretty rough. You will see well maintained ruins of some buildings, and can hike up to Kahekili's Leap (Warrior's Leap), where the King's men could prove their bravery - a 63 foot dive into the ocean, or walk around tidal pools at the shore. To get to these places, you need to hike down the rough trail that goes off to the right just after the picnic table. There are also a few old fishing houses down the road, and you can hike to them. If you walk out to the lighthouse you will get some great views of the cove and the cliffs down the coast. Here is a link to directions and photos of this location:
http://www.tripadvisor.com/ShowUserReviews-g29219-d519889-r67497961-Kaunolu-Lanai_Hawaii.html
Still another option is to visit Awalua. There is where you can see the 2nd shipwreck. This road can be rough, but has been reported in 2012 to be quite manageable. Here is a link to more info, pictures and directions:
http://www.tripadvisor.com/ShowTopic-g29219-i1684-k5191684-Lanai_Jeep_Rental_Where_to_Go_and_Timing_of_Same-Lanai_Hawaii.html
The Pocket Guide to Lana'i, available at most shops in town and at the resorts, has great descriptions of all these places with wonderful photos by Joe West, who lives and works on Lana'i. I would not expect one to be able to see all these sites in one day, so you will have to pick and choose, or just stay on Lana`i longer and rent the Jeep for a couple days.
And don’t forget to spend a little time in Lana`i City while you have the Jeep. There are fun shops, art galleries, the Lana`i Cultural Center, and good restaurants at which to eat or get takeout for a picnic.
-DrV