It's hard to find parking around Union Square. Your best bet would be on the east side. I would suggest you take public transportation.
There is metered parking along 14th street corridor. But public transportation is the easiest and cheapest option. That way you get to enjoy your visit without the worry of parking tickets, etc..
Honestly it's so much easier to take the train. However if you wanna park I'd look for street parking or a local garage
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