I'm a violin/viola teacher. I teach both Suzuki and Traditional methods. I think it's a great method for children especially. It emphasizes listening, memorization and parental involvement. The listening really helps the students develop their ears and makes it easier for them to learn the tunes and rhythms before they can read the music. The parental involvement is key too because with the parents' help with practice at home, the child will learn quicker and is less likely to develop bad habits.
Finding a teacher that's right for you and your child is the most important thing. You need someone who will encourage your child and make it fun for them but who enforces proper playing position, bow position, intonation, etc. Getting a good solid start is so important and saves frustration from having to break bad habits later on. Flexibility and the ability to personalize the lesson for each individual helps a lot too.
Some places make you sign on for a huge time and money commitment up front, like parents attending lessons first, and are a bit overwhelming to many. Of course if you put in that level of commitment, you're most likely going to see good results, but many people just don't have the time or money. You can get just as good or better lessons from the right private teacher.
As for cost, I have to say that around here the prices mentioned earlier are unheard of cheap for any type of music lessons. Also I tend to move a bit faster in my lessons and get them started on twinkles within the first few lessons (usually second) This is my personal preference because of the steep learning curve associated with starting stringed instruments (bow hold, posture, finger placement, etc) and it keeps the students excited. This of course is not at the expense of correct posture and bow hold

I am not an officially certified Suzuki instructor, but I grew up on the Suzuki method and am very familiar with it.
If you have any more specific questions, feel free to ask

I feel like this post is a little disjointed :LOL