The drive to Alstrom Point is a great day trip, accessible by most vehicles. You should plan on spending about 4-5 hours, unless you plan to spend the night.
There are plenty of camping sites at Alstrom Point, and very few are usually taken. There are no Services in the area so you will need to bring every you need with you.
A 2wd vehicle can usually do most of the trip under ideal conditions, but will only be able to make it to the 2wd overlook. High clearance and experience driving offroad is required to do the last 3 miles.
You should bring plenty of water, and enough food to stay the night. The combination of isolation, poor reception, and dangers associated with driving offroad can quickly turn a day trip into an involuntary overnight trip.
You should expect to not have reception for most of the trip. This means that gps systems that require internet to download the maps will not work. I strongly recommend downloading our pdf with a print out of the directions and photos of each turn. Included on the printable pdf are emergency contact information for towing companies, and visitor center information for road conditions and weather forecast.