Most of the time community classes aren't completely free, but they are inexpensive, often dance classes might cost about $10 per each lesson x 5 to 8 lessons. Summer classes would start in July, but check into them soon.
South Pasadena Community Services Classes
http://www.ci.south-pasadena.ca.us/parks/parks.html
Click on on Community Services Classes & Programs to download a PDF of the summer classes.
Belly Dancing, Hawaiian/Polynesian, etc.
LACC Community Services Classes
http://www.lacitycollege.edu/academic/departments/comsvcs/updating.html
Summer Catalog PDF
Belly Dancing, Jazz, etc.
Pasadena City College Extension Classes http://www.pcclearn.org/
Belly dancing, etc.
LA City Dept of Recreation and Parks
http://www.laparks.org/dos/parks/parks.htm
http://www.laparks.org/eregistration.htm
Good luck!