I commute from OC to LA, I average 70+ miles daily. 2/3rd of that is freeway and the other 1/3rd local streets. Street riding etiquette isn't that much different from local streets, but since you asked about local I'll talk about that.
I rarely split lanes if traffic is moving. 95% of my splitting lanes is coming to an intersection and looking ahead to see if I can squeeze in between the cars. If I can't I just wait in traffic like everyone else. However if I see that I have room I move up and position my front tire into the crosswalk, but my entire bike is not inside the crosswalk just the front tire. This does a few things:
1. It communicates to the drivers to my left and right that I am going to get out of their hair once the light turns green and that they SEE you.
2. Sticking out allows you to keep your eyes on the traffic lights, or if you know your streets you can see when the opposing direction stops so that you can take off.
3. It gives you a clear view of the cross streets for any possible red light runners. As a matter of fact I personally move a little further into the crosswalk when I know my light is about to turn green just so I can see that I'm clear.
The only exception to the above is if I lane split and come up to a busy crosswalk where lots of people are waiting or someone in a wheelchair, then I sit behind the line, but once ppl are clear I move up again for the reasons above. I don't do this if it's just one or two people walking.
I personally don't lane split single turn lanes. However for right turns, if the front car is going to go straight and holding up the vehicles behind them from turning right, then I squeeze onto the shoulder and right turn.
Double left turning lanes; I split if I can. My bike position is similar to the points 1,2,&3 above.
If I lane split either going straight or turning and for whatever reason I can't go any further and get stuck. I position myself in between all four cars. At a stop it is highly critical that drivers behind you can see you.