The characters can be found at the front of the park at opening. Around 11 or so they had beck to Shamu's Happy Harbor area.
My cousin works at SeaWorld and is a character wrangler. She works with all of them.
There are a lot of them including Shivers the Polar Bear, Petey Penguin, Dolly Dolphin, Shamu of course...and there is another penguin, an otter, a walrus and some others. They usually come out in pairs and there will be a photographer there for photo ops.
I got to hang out with some of the characters this X-mas and it was fun. Good luck on finding them.