I visited this site in May 2025. As mentioned, there is a brand new museum that is really well-done. There's interactive screens and buttons you can press to learn about the different reasons Çatalhöyük is important. For instance, Çatalhöyük showed evidence of a egalitarian society, with no difference in the treatment of men and women. No one home unit was more elaborate or larger than another, also seen as evidence towards this point. There is, additionally, a replica of the houses on site (pictured) that you can freely walk into and get a feel for what it might have been like thousands of years ago. Other facilities on site: cafe, bathrooms, gift shop, and lookout tower. I was a big fan of the museum and found it to be really interesting. The reason I didn't rate it higher is simply because there isn't much to see of the actual archeological part! When I was there, they said only 10% of the estimated remains had been excavated. Additionally, most of the findings (statues, tools, etc) in the museum are replicas; the real versions are in the Konya Archeological Museum. I don't personally mind all the replicas, but some might.
The main reason I wanted to make this review was to highlight that there is now a daily shuttle going to Çatalhöyük from Konya's city center (which is also a tentative site itself). The company is Dolash Konya City Tours, where they tell you it's a "guided tour" but it's only a transportation service. The cost was around 350 tl or $8-10 -- no reservation necessary. It leaves in the city center across from the Mevlana Museum at 1 pm everyday except Mondays. On Fridays there is prayer and if that goes long, you will probably leave more around 2 pm (speaking from experience). However, the bus driver gave us 2 full hours at the WHS, which was more than enough, and we got back to the city around 5 pm. To get to Konya, you can fly or take advantage of the high speed trains, which connects Istanbul to Konya in only 5 hours.
It's hard to not compare this WHS to Göbekli Tepe. However, what Göbekli Tepe lacked in an extensive on-site museum, it made up for with impressive archeological remains. Çatalhöyük's museum is amazing, but Göbekli Tepe is still my favorite Turkish Neolithic site.