The highlight for my son was getting to pet a real shark - in this case a very well-behaved Swell Shark (he was about a yard long). A kindly staff member showed each visitor the appropriate way to do it, and offered a hand towel afterwards for drying off arms. I tried it too and I have to say, it was strangely thrilling. In a low-key way. There was also a series of smaller saltwater basins for petting starfish and anemones, with a staff member on hand to answer questions (there were many).
There is a variety of exhibits on marine science - I saw very few children in this section however - it just couldn't compete with the fantastic animal life in the next room.
The Center is nicely situated on a bluff overlooking the Pacific; be sure to take a stroll during your visit. You will not be able to miss the incredible (and beautiful!) blue whale skeleton installed outside. If you're hungry, there is a nice cafe in the neighborhood: Kelly's French Bakery (at the corner of Swift and Ingalls Streets). We sat outside in the sunshine and ate a delicious little spinach tart. Perfect afternoon!