If you're in Monterey with kids (especially younger ones), you absolutely have to go to the Dennis the Menace Park on Pearl Street. It isn't far from the Aquarium and is absolutely fabulous. So fun, HUGE, and great for kids. This is one of the best playgrounds I've ever seen and my kids didn't want to leave.
The Cannery Row area is full of shops and restaurants, but is a bit touristy to me. I love heading to the Historic District around Alvarado Street. There's a great Greek Restaurant that I love called Epsilon Fine Greek Restaurant that's amazing, but if that's not great for your family, you will find other restaurants in that area.
At the end of Alvarado Street is Portola Plaza. From here, you can walk along the water's edge on a beautiful path for miles to Lovers Point Park and beyond. It's truly an absolutely gorgeous walk and the kids will get some running around time and will love seeing sea lions out there in the wild. It's so cool.
If the season is right and you have time, the whale watching trips are wonderful. You may see several varieties of dolphins and whales. May be you need two days. :)
I have two of my own munchkins, and we love playing in Carmel By the Sea / Monterey . We're actually developing a new entertainment dashboard to help fellow parents find family-friendly things to do (www.GoWiLi.com), but since it isn't quite ready, here are a few suggestions:
1) Monterey Farmers Market (it's on Friday's, but works for an extended weekend).
2) Fairs and Festivals - for example, there's a holiday gift fair nearby this weekend run by the Santa Cruz Mineral and Gem Society, with jewelry, beads, fossils, geodes, etc.
3) Sunday Seaside Crafts - through the end of November, at the Seymour Marine Discovery Center (Long Marine Lab)
4) Old Fisherman's Wharf in Monterey doesn't compare to SF, but it's a nice stroll.