They've already launched from California, at Vandenberg AFB. They've begun constructing a drone ship for landing future rockets launched from Vandenberg, named Of Course I Still Love You (the one currently in use for KSC launches is called Just Read the Instructions).
And yes, they are currently constructing a new spaceport in Texas near Brownsville at the far southeastern corner of the state. Completion and first launches are anticipated in 2016. I'd guess they might use the current drone ship for landings from that one as well, but a lot can change in 2+ years so we'll have to see.