C.A.
www.LongBeachBallet.com has classes for three year olds. One class per week for about $56. As an alternative, you could get some do-it-yourself tapes/DVDs and make this a fun mother/daughter time together. http://www.musicworksunlimited.com/ has some.
Personally, I think three is too young for structured activities. Kids should be encouraged to play and use their imagination. I really like the idea of a time you set aside just for the two of you to have fun. What do you think?