Aikido certainly can be called a martial art, but not, I think, a dance routine. It is graceful and beautiful to watch for some people, though.
Saying you want to learn self-defense is a bit vague, but if you want some quick "take-downs", aikido will not be for you. It generally takes a long time to be effective, and the technique can be subtle.
With the right teacher, aikido is much more than self defense. It is a budo whose aim is the purification of the self. I recommend you attend dojos which teach things that interest you, and get a feel for which will work best for your particular interests.