There's valet ... And paid lots all around ... But I'm not sure if they are affiliated with The Met.
Also, consider using a pre paid parking app with will discount parking and provide a map with parking locations near the Met.
There are both affiliated and non affiliated paid lots, though usually at a premium price point. Street parking depends on time and amount of street construction. Broad st line is another option.
Every time I park a few blocks away a have no problems finding a street spot.
There are 5 or so in proximity. I believe you can pre-pay through the venue.
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