I taught for Arthur Murray for a year, and would not recommend it. If you're not happy, find another studio.
Every Arthur Murray studio is a little different, so it really depends on the franchisee owner on what kind of quality you're going to get. The advantage of going to an Arthur Murray or Fred Astaire is that you know that your instruction will have to meet certain standards in order to be accredited. When you're first starting and don't know how to judge dance quality this is a big deal. The studio I was at trained us really well on how to teach in a simple way and break everything down so that any beginner could easily learn no matter how awkward they were.
That being said, Arthur Murray is good for beginning students, but most Arthur Murray's will not progress you to more than just a decent social dancer. Even our "gold" students could barely lead and follow.
Arthur Murray hires instructors based on friendly personalities and looks. No prior dance experience is necessary. They train them pretty intensively before they are allowed to teach, so again, for teaching beginners they are pretty good. However, at the studio I worked at, once they receive their initial training, the amount of training they receive afterwords is minimal. We had a dance session once a week where a senior teacher would teach a group class to the rest of the staff. Also, coaches come into town around once a month, and give group class instruction to the teachers. You had the option of getting a private coaching, but it was extremely expensive and the instructors don't get paid enough to be able to easily afford it. At my studio, all the instructors were either living at home, had some other source of income, or were on food stamps to make ends meet.
I left because I wasn't progressing in my dance, was making next to nothing, and I was tired of being manipulated by our studio manager. In order to get us to stay, management would often publicly humiliate us in order to shame us and tear our confidence down. They would also tell us that "some day" we could make management, and then we'd be making more than "engineers". Somehow the staff bought into it, and some of them had been there for over 7 years and were still struggling as teachers. I also did not feel that we were being trained on how to give the students what they wanted; we were being trained on how to convince the students to want what we had. To an extent, I understand that, but we definitely were being trained on using manipulative tactics to get students to do buy into doing more, and I was uncomfortable with that.
Teachers were required to tell everything students told them to the studio owner and other staff that would be working with them. One of the things we often did during our daily meetings was a simulation where one instructor would pretend to be a student and the other staff would take turns asking personal questions to the "student." We would get chastised if we did not know the answers to these questions. I once refused to pose as a student because I felt very uncomfortable breaching their confidence in this way, and I got into HUGE trouble for it. I left shortly after. If you tell something to one teacher, you're telling it to them all.
Again, I want to emphasize that not all Arthur Murray studios are the same. The studio I was at was particularly bad. Other ones are MUCH better than that.