Actually, there are spots that open only after 10am specifically for people heading in after the morning rush (i.e. tourists). I have never had a problem finding a spot posting there. I think it's 10 am, but check the site. I want to say it's like $5 maybe? It wasn't much.
Depending on the day there are usually parking spots available. It's $4.65 for all day. You might have to do a little searching and probably would have an issue if it were a special event.
It's practically impossible to get spot there when actually need one. Park somewhere else and catch an Uber.
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