Focus on these five main areas when considering music lessons for either your child or yourself. 

1) Safety
Be sure the studio is licensed and certified to be in operation.  This means that the teachers have undergone background checks, the facility has been inspected, and all of the necessary requirements have been filled at the city and state level.
If a studio has the proper licensing & certification to be in operation, the information should be made very clear on their brochures & website.  As well, the licenses should be displayed in the reception area of the facility. 
2)  Teacher Credentials
Are the teachers degreed?  Do they have teaching and performance experience?  You're paying tuition and are entitled (and should demand) that the instructor is qualified to be working with either your child or you.
3)  Tour the Place
Are studio tours available?  This should be standard but, unfortunately, not all studios offer this.  Quite simply, you should have the option to tour the studio, meet with the owner, and make your decision.
4)  Payment Policy
Be sure you know what the payment policy is; this information should be made available to you from the beginning.  Paying month to month is fair and reasonable.  There are some studios that require you to pay for 6 months (or more!) in advance for lessons.  But keep in mind that if you do pay month to month, fees may be applied for late payments. 
5)  Prices
Speaking of paying...what are the studio's prices?  Be sure to price around and take into consideration the following:
location
flexibility (Is there a cancellation policy? 24-hours' notice is reasonable, but some studios are more strict and require several days notice or don't even offer make-up lessons.)
reputation
qualifications of teachers

Best of luck on your journey to becoming a music maker!
Ellen Bartolozzi
Owner, Bella Angel Music