I liked it well enough to visit there with a friend who was visiting just before I married. That must have been about 15 years ago, and boy has the NHM changed since then!
I took two of my kids there today, and we had a blast. Very few exhibits remained from my last visit: Megamouth, the coelacanth, and the oarfish still greet you in the lobby (Megamouth is just as ugly as I remembered). The bird exhibit looked more or less as I remembered it, as did the dioramas of African mammals and North American Mammals.
The improved Dino Hall and Age of Mammals exhibits lived up to the hype, especially the dinosaur exhibit. Many interactive stations invite visitors to investigate the details of each display. There are neat explanations of how science is done, for example how continuing research changes our perceptions over time. The new gardens -- one for edibles and one for nectar producing flowers (which lure butterflies and hummingbirds) -- are gorgeous, although it was too hot today to linger in them. On a cooler day, there are lots of inviting spots to sit and rest and watch the animals that visit the plants. The gem exhibit has been improved, but may still disappoint you if you've visited the Smithsonian or the like.
The Becoming L.A. exhibit exhibit lacked the structure and storytelling that would have taught visitors more about how our region developed over time. It replaced an out-of-date exhibit about the American Indians of the region, but now the Chumash and the Tongva are hardly mentioned at all. Instead, the exhibit skips almost immediately ahead to the missions and ranches. And far too much time is spent on the last hundred years. I didn't know what to make of some artifacts because they were so out of context. There are some nice touches: the Latino experience was worked into the exhibits in several places, often telling heartbreaking stories, and some of the artifacts on display were neat. However, I felt let down by this exhibit.
After that disappointing experience, we went to the newest addition to the NHM, the Nature Lab. This was by far my favorite part of the museum. Not only was this a truly interactive experience, but it had exactly the qualities (structure and storytelling) lacking in the Becoming L.A. exhibit. The Nature Lab invites museumgoers to introspect about their experiences with wildlife in SoCal and teaches volumes about our environment. By following the memories of scientists ("I remember the time when..."), we are drawn into the experience of observing wildlife and plants. Locals will appreciate learning about the birds in our area (I finally learned that a species I've admired recently is called the "Black Phoebe.") including a whole display about the green parrot flocks. Also, a very useful display explained the differences between rattlesnakes and gopher snakes. (I say "useful" as we often see snakes while hiking in our area, including on last Sunday's hike.)
Overall, it was a delightful visit to NHM. I highly recommend it as a destination -- it will take most of the day to see everything. We paid full price, but if you can wait until September, there will be free days every Tuesday that month, and one Tuesday a month thereafter. You can also get a discount if you are a teacher or if you take the light rail to get there. (We tried to do that, but the park and ride was full at the Culver City station.)