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After browsing and purchasing a few things I finished up by taking pictures and stopping to talk with someone at the Farmer's Market Booth. I asked them, too, if they knew where more bike racks were and they didn't , but guessed there would be some near REI. I pointed out that this was something cyclists visiting the market might want to know and he agreed it would be good to have that information.
I unlocked my bike and did a ride around several different blocks to find that the next nearest bike racks were across the street from REI. There are three along that road, all able to hold two bikes each. They were half full at around 4 pm. I figure they will fill up more in the evening when people are coming to eat at the local restaurants. With the market running till 7 pm I hope there will be enough bike spaces for everyone - once the market gets better known I wonder if there will be. Many of the restaurants in the area don't have any bike racks nearby at all.
I have to admit I was surprised to not find bike racks at the Cascade play area. Maybe they were hidden somewhere?
For Mark and I, cycling would be the main way we would get to the South Lake Union neighborhood, possibly combining bikes and the street car. At this point we won't find many places to safely lock our bikes while we are there. There is a serious need for more bike racks in the area, especially with a new Farmer's Market to come to and an increasing number of interesting restaurants.