parking near the convention center during popular conventions can be outrageous, and can range from $20-50 per day. the metro blue line (light rail) has a stop at the center; it's $1.25 per person, one way. LA dash (a downtown-only bus service) also stops there, for $0.25 per person.

unlike chicago, public transit options in LA are limited unless you are willing to invest the time both in learning the bus routes and in making multiple transfers. there is nothing for kids to do downtown, particularly in the evening. but if you're staying downtown, the red line (subway) can take you directly to hollywood and universal studios/citywalk.

if you want to visit the beach, you will either need a car or stay close by. one option to consider is santa monica, which has both a beach and the third street promenade. santa monica also has a "big blue bus" which has express service to downtown LA.