This is a fantastic farmer's market, however it is CROWDED. Small wiggly children can easily be lost and it is definitely not a good place for a stroller. However, there is plenty of fresh produce, flowers, bread, and treats as well as food vendors. Many musicians grace the area; typically something for everyone. Be aware that there are several balloon-animal artists and your child is bound to want one (choking hazards be damned). You may consider parking several blocks east (near the mall or even waterfront) and take the MAX train there due to a parking shortage (as well as the additional fun factor of riding the train.)
We head to the farmer's markets a lot, and this is the biggest one (and one of the best I have been to in the US). Some of the best organic produce ever is sold here. The selection is amazing and there is something for everyone. The vendors change as different produce comes available. There is also other product that is sold as well as (crafts, ice cream, meats). There is also entertainment which the kids always love to dance to. We love going so our son learns about fresh food, where they come from and is involved in what he is eating. So far, we don't have a picky eater and he tries everything. I think it is a nice way to get the kids learning, and will get him excited about our own gardens.
The market happens twice a week downtown, and at several other locations at other times. Check the website fore details.