Someone I've never heard of before and know little about - California state senator Sam Aanestad - might be the best choice (so far) for Lt. Governor. Based only on a quick glance, his immigration position seems acceptable [1], but the much more important factor is who else is vying for the job:

* Fellow Republican Abel Maldonado is his opponent in the primary. Maldonado is who Arnold Schwarzenegger wants for current Lt. Gov., which pretty much disqualifies him from consideration.

* One of the Democrats in the running is Los Angeles City councilwoman Janice Hahn. Back in 2004 she responded to a raid of an illegal alien drop house raid by saying, "The federal government is turning a blind eye to what's happening at the border". However, I suspect she's not on this site's side for the most part.

* Even worse than the other two, Gavin Newsom has thrown his hat into the ring. The only good thing that can be said about him is that he isn't as strong a supporter of illegal immigration as some of those on the San Francisco Board of Supervisors, but that's not saying much.

[1] Per this, he opposed the 2006 decision by some of his colleagues to support the "Great American Boycott", an immigration march. And, per this from 2008:

Senator Samuel Aanestad voted NO to passed Bill SB 1160, Driver's Licenses for Undocumented Immigrants, a bill that requires the Department of Motor Vehicles to issue driver's licenses to individuals allowing them to drive legally although it does not prove legal residence or citizenship. The bill specifies that the Department of Motor Vehicles cannot begin issuing these licenses until the Secretary of Homeland Security approves California's plan. This bill requires California to comply with the requirements of the federal Real ID Act of 2005 for the issuance of drivers licenses and identification (ID) cards by May 12, 2008. The Real ID Act authorizes the issuance of driver's licenses and ID cards to undocumented immigrants, but the license or ID card may not be used for any other official purpose, and must be a unique color or design.