I visited this WHS in July 2023. We were staying in Geneva with a cousin who was working at CERN, and I had heard about La Chaux-de-Fonds being famous as the place of origin for Switzerland's rich watch-making history, so we planned an entire daytrip around going out to the town in the North. I'm sad to say that it is dubious whether all of the effort was worth it.
The main goal of our trip was to see the watch-making museum. According to the Internet it was to be open and operating at the hours we were visiting. However, after multiple hours of travel getting out to this town and navigating on foot from the train station to the museum – we found the museum closed. Apparently, the town had endured a huge windstorm a couple of days before which had knocked down trees and branches all over the city. There was tape covering one stairway that lead to the museum, but nothing offically blocking off the ways of accessing it. Curiously, there were no signs or anything indicating the museum was properly closed, and we couldn't tell for sure whether it was not operating or we were just looking at the wrong location for an entrance. We encountered other confused groups of tourists looking to get into the museum, and after twenty minutes of wandering around or so we finally gave up. No one had written anything online indicating that the museum was temporarily closed.
At least we could make the most of our journey by visiting something else in the town, right? Well, it turns out there's not a lot to do outside of the watch museum. We searched around the town (and checked online sources) for anything else we could spend our remaining hours doing but there wasn't a lot. The few options that did exist were all closed because we were visiting on a Sunday. We entered a small visitors center/local history museum which was neat and gave us a bit more context for the town by projecting a video onto the ground and mixing that with some signs. However, it was quite small, and other than that we simply had the option to wander the grid-like streets and appreciate the architecture built specifically for the watch-making industry.