It may seem like a long way to go, but just get on the 7 to Queens and do it. There's a dumpy taxi stand and some abandoned buildings but yes, you're in the right place. That old public school, the OG public school actually, PS1, is an afternoon dying to be wasted. Free admission with your MoMA stub too.
Openings here can be very pretentious but you'll likely rub shoulders with the artists making the working you're looking at and you can't get that at the Met. You may leave frustrated, angry and totally confused about what you've just ingested but it's art, it's contemporary art and it will stick with you at the very least.
Some of the permanent installations are fantastic, the special shows are typically packed. If you're in NYC for a week or so try to plan your visit around an event at PS1 as opposed to an empty Tuesday morning. Highly recommended if you're not an idiot who hates to think.