Although the site is officially called Willandra Lakes, it's Mungo National Park (mostly within the boundaries) that is the main attraction and the focus for most visitors. Other parts of the WHS are no more impressive and quite inaccessible, other than views from the roads on the way in. Mungo makes up most of the site, and this is all you'll need to worry about visiting.
For many Australians, Mungo is considered to be 'in the middle of nowhere', but it's actually not too hard to access by car from Melbourne or even Adelaide. From Sydney, it's become a popular stop on a road trip to nearby (by Aussie standards) Broken Hill. Although a 4WD/AWD is recommended, you will be able to get to the site with a normal 2WD if the weather has been good, which means the unsealed roads will be in a good condition. But one of the popular activities - driving the Mungo Track - is best done with a 4WD/AWD.
The geological story of Mungo National Park is fascinating - in short, large lakes dried out about 14,000 years ago and the sand left around the edges has gradually been sculpted into incredible shapes by wind and rain. The most impressive example of this is known as the Walls of China. On your own, you can see them from viewpoints on the boardwalk, but you can walk out onto the sand if you're with an organised tour. I would highly recommend doing this at sunset.
The other significant aspect of the site is the discovery of human remains arranged in ritual burial positions that have been dated to about 40,000 years ago! However, there is nothing to see directly about this, although you'll learn some of the story at the information centre.
There are several walks to do at Mungo National Park, as well as driving the Mungo Track, and exploring some of the pastoralist history. I think it's certainly more than a day trip, even though I know some tour companies do offer that from the nearby city of Mildura. The nice accommodation on site is expensive, but you'll get a lot more out of staying overnight and seeing things over about 1.5 days. There are camping options, which are much cheaper.