I'm a native Lodian!
Typically the Mokelumne River opens on January 1st each year. It's a tail water with pretty good access and only about a 20 minute drive. I haven't looked into the details or regulations for 2016, but I'm 99% sure it will be open.
There are trout and steelhead. Here's a trip report from a couple years ago. I've only fished it a few times.
viewtopic.php?f=9&t=8953As Wanderingblues said the Delta is right here in our backyard, but in my experience it's pretty tough to access without a boat.
There's also the Consumnes, another tailwater, but given the drought and reservoir levels I expect it to either be closed or just poor fishing.