The most common form of dance logo is a dancer's silhouette. There's a reason for this, which is that the silhouette can probably be universally recognized as representing dance. However, there is a myriad of ways in which you can make the logo for your dance studio or dance institute stand out from the rest.
You first have to pinpoint just what the brand message for your logo would be. From there, you would decide upon the design style, symbols, colors, etc. For instance, if you're teaching ballet at your studio, a ballerina's silhouette would be the one to go for. Bright colors like hot pink, teal, and electric blue would be the best ones to choose here, as dancing is a passionate and striking activity. If you want to do something a bit different, a pair of ballet shoes would make a great dance logo as well.
Your target audience may also be an inspiration behind your unique dance logo. If you want to target couples, for example, your logo could depict a couple conducting a ballroom dance. The clothing styles and position of the dancers would let potential customers know what you're offering and attract them at the same time. The dancers' angle might also be in such a way that the name of the company is highlighted. This would help to keep the logo stuck in a person's mind.
Since dancing is usually about evoking feelings and emotions, you can have a somewhat fancy, cursive font with your logo here. However, make sure it's readable from a distance. Lucinda Handwriting could be one viable example of a font you may use with a dance logo.
If you want to ensure an effective dance logo for your studio you should seriously consider hiring a professional logo designer. This would help to minimize any risk and enhance the chances of success.