So many, many wonderful restaurants downtown. Don't be afraid to go into the city - it's really easy to navigate. There are some neat flamenco places there - you could get dinner (tapas) and then see a show afterwards. I think Cafe Sevilla was one of them. The kids might enjoy that.
For kid-fun things - legoland, the zoo, and the wild animal park are tops! Never been to SeaWorld, but I bet it's great too. Depending on when you go, the San Diego fair will be running at the Del Mar track at the end of May beginning of June - super fun.
There's a pier at Ocean Beach - if the kids like fishing.
La Jolla has a really pretty paved walk to do along the ocean. Good place for kids to run and get their energy out while adults mosey
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Mission Bay Park is also a fabulous place to take the kids. Lots of green space - everyone picnics there. Rent some bikes and bike all on their paved trails. Some really nice playgrounds there too.
I love SD. Only lived there for 1.5 yrs but had a great time!