What are some honest non-for-profit charity programs I can participate in Los Angeles, CA and/or Mexico (Tijuana area)?

There is an organization in Tijuana called Esperanza International that does charity house building. Here is an article by an American student about his experience with them.

It is not uncommon for church groups in the Southwest to visit Mexico for charitable reasons. Calvary Chapel of Downey, for instance, collaborates (or at least, it used to) with an orphanage outside of Tijuana, which is in turn used as a base for helping the surrounding area. I don’t know if they build things, though.

Habitat for Humanity is everywhere. They will use your time and talent as much as you would like to share.

you could also get involved with “save the greyhounds” programs. Plenty of former racing greyhounds in the region need homes.