Butler Hall is a very nice prewar building which was a graduate/faculty residence in my time. It was one of the classiest buildings run by Columbia in the immediate vicinity of campus. The penthouse was occupied by an absolutely wonderful French restaurant called Terrace in the Sky, now gone, alas. It was one of NYC’s best reasonably priced fine dining experiences, with awesome views.
Re your question about vermin, the Upper West Side in general is well known for large active roach and rat populations. Mice can be found wherever there’s something they can eat. Bedbugs were not in my experience but there’s been a lot of publicity about Manhattan hotels with infestations. I’m sure Butler Hall these days is no roach trap but if there’s a significant problem, university maintenance would bring in an exterminator.
You’re probably pretty lucky to get in Butler Hall, but IDK the relative desirability of the dorms these days. Perhaps a current student could weigh in.