I visited this WHS in July 2019 as a very convenient stopover while driving from Lake District National Park towards Edinburgh. This WHS can be seen as one of a series of similar industrial sites in the UK, namely Derwent Valley Mills, Saltaire and New Lanark. All three WHS aren't wow destinations or top WHS but all offer an informative visit to how UK's industry and working conditions looked like during the last century or so.
Of the three I'd pick the Derwent Valley Mills as it is well presented and you can see some machinery still working. Even though my least favourite is Saltaire, New Lanark wasn't much better. At least there were a couple of information boards and I was surprised by the roof garden which was so ahead of its time. But apart from that, everything else was pretty much empty or geared mostly at school outings not WH travellers. The trail to the Falls of Clyde was pleasant enough mostly because I always had wanted to visit them (because of my name though!). If you're staying over in New Lanark during the peak months, you can also arrange a night walk at the visitor centre to spot the resident badgers.
There's a big free of charge visitor parking lot just before going down towards New Lanark and the panoramic view from there is worth having. However, after a couple of photos, you're better off walking back to your car and parking near the visitor centre itself (near the yellow metal gate with the UNESCO symbol), again free of charge. I also tried the icecream but after having visited Lake District, I thought it was nothing special. The supermarket-like store has a small section with UNESCO related stuff for sale and I managed to find the nomination dossier for sale. It will be a good read also to compare UK's industrial WHS with other similar WHS around the globe.