I've been there with other AU'ers a couple of times, once just to check out the museum and neighborhood and a second time for the Candlelight House Tour and associated holiday party.
There is some information about the buildings and neighborhood at this website, if you haven't seen it already:
http://www.pullmanil.org
The museum was small, but nice. They had quite a few interesting pieces, and everyone was friendly and eager to answer questions. There's also a 10-15 minute video that runs before you walk through the museum.
I'm not sure if the church, hotel, etc. are open all day. I believe you can see those as part of a tour. I'd love to do that some day.
The neighborhood itself is "sleepy". I remarked that I felt like we were walking around a movie set. I didn't see a single person or moving vehicle the entire time we were there. We didn't feel unwelcome or "watched", though. As I learned during the Candlelight Tour, the residents of the neighborhood are quite welcoming and happy to have people visit.
If you have time, you may want to head up to Graceland Cemetery. Pullman is buried there, along with many other big names in Chicago. The cemetery is home to some pretty famous graves and a few urban legends. It's one of my favorite Chicago topics.
Anyway, Pullman's grave is remarkable not just in its size, but in its history as well.
Since Pullman died only a few years after the railroad strike, his family was worried protestors or former workers would dig up his body. When they buried him, they put him in a lead-lined casket and then sealed the casket in concrete. After he was lowered into the grave, the concrete slab was covered with asphalt, tarpaper, and more concrete. THEN, they added steel rails and more concrete.
His gravesite was designed by the same architect who designed the community of Pullman. Here is a link to a picture:
https://en.wikipedia.org/wiki/George_Pullman#/media/File:George_Pullman_tomb_by_Gerald_Farinas.JPG