I dont really see the problem - without having to go through all of the city red tape and government BS - just bring some of your own tables and chairs (so you dont have to rely on availability if the ones they have there). Its just a small party not some crazy event.
You may want to that may guarantee that you get a table rather than just a spot on the grass.
Call the city tonmake sure what you want to set up is ok or if you need a permit
Is better if you call the city to find out.
Certainly you would need to know if there are any other major events that you might not want to collide with .
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